Mutational analysis: A joint framework for cauchy problems in and beyond vector spaces

Lecture Notes in Mathematics

Volumn 1996, Issue , 2010, Pages 1-516

  Lorenz, Thomas ^a  

^a GOETHE UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77953173733     PISSN: 00758434     EISSN: None     Source Type: Book Series    
DOI: 10.1007/978-3-642-12471-6_1     Document Type: Article

References (190)

1. Aletti, G., Bongiorno, E.G. & Capasso, V. (2008): A set-valued framework for birth-andgrowth process, submitted preprint at arXiv:0805.3912v1
2. Alt, H.-W. (2006): Lineare Funktionalanalysis, Springer, fifth edition
3. Ambrosio, L. (2008): Transport Equation and Cauchy Problem for Non-Smooth Vector Fields, in: Dacorogna, B. & Marcellini, P. (Eds.), Calculus of Variations and Nonlinear Partial Differential Equations, Springer, Lecture Notes in Mathematics 1927, pp.1-41
4. Ambrosio, L. (2004): Transport equation and Cauchy problem for BV vector fields, Invent. Math. 158, no.2, pp.227-260
5. Ambrosio, L., Fusco, N. & Pallara, D. (2000): Functions of bounded variation and free discontinuity problems, Oxford Mathematical Monographs
6. Ambrosio, L., Gigli, N. & Savaŕe, G. (2005): Gradient flows in metric spaces and in the space of probability measures, Birkḧauser, ETH Lecture Notes in Mathematics
7. Antosiewicz, H.A. & Cellina, A. (1977): Continuous extensions of multifunctions, Ann. Pol. Math. 34, pp.107-111
8. Antosiewicz, H.A. & Cellina, A. (1975): Continuous selections and differential relations, J. Differ. Equations 19, pp.386-398
9. Artstein, Z. (1994): First-order approximations for differential inclusions, Set-Valued Anal. 2, pp.7-18
10. Aubin, J.-P. (1999): Mutational and Morphological Analysis : Tools for Shape Evolution and Morphogenesis, Birkḧauser 1999
11. Aubin, J.-P. (1997): Dynamic Economic Theory. A Viability Approach, Springer
12. Aubin, J.-P. (1993): Mutational equations in metric spaces, Set-Valued Anal. 1, pp.3-46
13. Aubin, J.-P. (1992): A note on differential calculus in metric spaces and its applications to the evolution of tubes, Bull. Pol. Acad. Sci., Math. 40, no.2, pp.151-162
14. Aubin, J.-P. (1991): Viability Theory, Birkḧauser
15. Aubin, J.-P. & Cellina, A. (1984): Differential Inclusions, Springer, Grundlehren der mathematischen Wissenschaften 264
16. Aubin, J.-P. & Da Prato, G. (1998): The viability theorem for stochastic differential inclusions, Stochastic Anal. Appl. 16, no.1, pp.1-15 (Pubitemid 128692549)
17. Aubin, J.-P. & Da Prato, G. (1990): Stochastic viability and invariance, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 17, no.4, pp.595-613
18. Aubin, J.-P., Da Prato, G. & Frankowska, H. (2000): Stochastic invariance for differential inclusions, Set-Valued Anal. 8, pp.181-201
19. Aubin, J.-P. & Frankowska, H. (1990): Set-Valued Analysis, Birkḧauser
20. Ball, J.M. (1977): Strongly continuous semigroups, weak solutions, and the variation of constants formula, Proc. Am. Math. Soc. 63, pp.370-373
21. Bangerth, W. & Rannacher, R. (2003): Adaptive finite element methods for differential equations, ETH Z̈urich, Birkḧauser
22. B́arcenas, D. (1991):Weak compactness criteria for set-valued integrals and Radon-Nikodym theorem for vector-valued multimeasures, Czech. Math. J. 51 (126), pp.493-504
23. Bardi, M. & Capuzzo-Dolcetta, I. (1997): Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations, Birkḧauser
24. Barles, G., Soner, H.M. & Souganidis, P.E. (1993): Front propagation and phase field theory, SIAM J. Control Optim. 31, no.2, pp.439-469
25. Barron, E.N., Cannarsa, P., Jensen, R. & C. Sinestrari (1999): Regularity of Hamilton-Jacobi equations when forward is backward, Indiana Univ. Math. J. 48, no.2, pp.385-409
26. Bauer, H. (1992): Mass- und Integrationstheorie, de Gruyter
27. Beer, G. (1993): Topologies on closed and closed convex sets, Kluwer
28. Bellettini, G. & Novaga, M. (1998): Comparison results between minimal barriers and viscosity solutions for geometric evolutions, Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV.Ser. 26, no.1, pp.97-131
29. Bellettini, G. & Novaga, M. (1997): Minimal barriers for geometric evolutions, J. Differ. Equations 139, no.1, pp.76-103
30. Bogachev, V.I. (2007): Measure theory, Vol.II, Springer
31. Calcaterra, C. & Bleecker, D. (2000): Generating flows on metric spaces, J. Math. Anal. Appl. 248, no.2, pp.645-677
32. Cannarsa, P., Da Prato, G. & Zoĺesio, J.-P. (1989): Evolution equations in non-cylindrical domains, Atti Accad. Naz. Lincei, VIII. Ser., Rend., Cl. Sci. Fis. Mat. Nat. 83, pp.73-77
33. Cannarsa, P. & Frankowska, H. (2006): Interior sphere property of attainable sets and time optimal control problems, ESAIM Control Optim. Calc. Var. 12, no.2, pp.350-370
34. Cannarsa, P., Frankowska, H. & Sinestrari, C. (2000): Optimality conditions and synthesis for the minimum time problem, Set-Valued Anal. 8, no.1-2, pp.127-148
35. Cannarsa, P. & Frankowska, H. (1991): Some characterizations of optimal trajectories in control theory, SIAM J. Control Optimization 29, no.6, pp.1322-1347
36. Cardaliaguet, P. (2001): Front propagation problems with nonlocal terms II, J. Math. Anal. Appl. 260, no.2, pp.572-601
37. Cardaliaguet, P. (2000): On front propagation problems with nonlocal terms, Adv. Differ. Equ. 5, no.1-3, pp.213-268
38. Cardaliaguet, P. & Pasquignon, D. (2001): On the approximation of front propagation problems with nonlocal terms, M2AN, Math. Model. Numer. Anal. 35, no.3, pp.437-462
39. Caselles, V., Catt́e F., Coll, T. & Dibos, F. (1993): A geometric model for active contours, Numerische Mathematik 66, pp.1-31
40. Castaing, C. & Valadier, M. (1977): Convex analysis and measurable multifunctions, Springer
41. Catt́e F., Lions, P.-L., Morel, J.-M. & Coll, T. (1992): Image selective smoothing and edge detection by nonlinear diffusion, SIAM J. Numer. Anal. 29, no.1, pp.182-193
42. Ćea, J. (1976): Une ḿethode nuḿerique pour la recherche d"un domaine optimal, in: Glowinski, R. & Lions, J.L. (Eds.), Computing methods in applied sciences and engineering. Part 1, Springer, Lecture Notes in Economics and Mathematical Systems 134, pp.245-257
43. Chen, Y.G., Giga, Y. & Goto, Sh. (1991): Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations, J. Differential Geom. 33, no.3, pp.749-786
44. Chen, Y.G., Giga, Y. & Goto, Sh. (1989): Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations, Proc. Japan Acad. Ser.A Math. Sci. 65, no.7, pp.207-210
45. Clarke, F.H. (1996): A proximal characterization of the reachable set, Syst. Control Lett. 27, pp.195-197
46. Clarke, F.H. (1983): Optimization and Nonsmooth Analysis, Wiley
47. Clarke, F.H., Ledyaev, Yu.S. & Stern R.J. (1997): Complements, approximations, smoothings & invariance properties, J. Convex Anal. 4, no.2, pp.189-219
48. Clarke, F.H., Stern, R.J. & Wolenski, P.R. (1995): Proximal smoothness and the lower-C2 property, J. Convex Anal. 2, no.1/2, pp.117-144
49. Conway, E.D. (1967): Generalized Solutions of Linear Differential Equations with Discontinuous Coefficients and the Uniqueness Question for Multidimensional Quasilinear Conservation Laws, J. Math. Anal. and Appl. 18, pp.238-251
50. Cornet, B. & Czarnecki, M.-O. (1999): Smooth normal approximations of epi-Lipschitzian subsets of Rn, SIAM J. Control Optim. 37, no.3, pp.710-730
51. Crandall, M.G., Ishii, H. & Lions, P.-L. (1992): User's guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc. (N.S.) 27, no.1, pp.1-67
52. Crandall, M.G. & Lions, P.-L. (1983): Viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc. 277, no.1, pp.1-42
53. Da Prato, G. & Frankowska, H. (1994): A stochastic Filippov theorem, Stoch. Anal. Appl 12, no.4, pp.409-426
54. De Giorgi, E. (1994): Barriers, boundaries, motion of manifolds, Lectures held in Pavia
55. Delfour, M. & Zoĺesio, J.-P. (2001): Shapes and Geometries: Analysis, Differential Calculus and Optimization, SIAM, Advances in Design and Control
56. Delfour, M. & Zoĺesio, J.-P. (1991): Velocity method and Lagrangian formulation for the computation of the shape Hessian, SIAM J. Control Optim. 29, no.6, pp.1414-1442
57. Demongeot, J., Kulesa, P. & Murray, J.D. (1997): Compact set valued flows. II: Applications in biological modelling, C. R. Acad. Sci., Paris, Śer. II, Fasc. b 324, no.2, pp.107-115
58. Demongeot, J. & Leitner, F. (1996): Compact set valued flows. I: Applications in medical imaging, C. R. Acad. Sci., Paris, Śer. II, Fasc. b 323, no.11, pp.747-754 (Pubitemid 27124985)
59. Diekmann, O., Gyllenberg, M, Huang, H., Kirkilionis, M., Metz, J.A.J. & Thieme, H.R. (2001): On the formulation and analysis of general deterministic structured population models: II. Nonlinear theory, J. Math. Biol. 43, pp.157-189.
60. Diekmann O. and Getto P. (2005): Boundedness, global existence and continuous dependence for nonlinear dynamical systems describing physiologically structured populations. J. Differ. Equations, 215, pp.268-319.
61. Diestel, J. (1977): Remarks on weak compactness in L1(μ,X), Glasgow Math. J. 18, pp.87-91
62. Diestel, J., Ruess, W.M. & Schachermeyer, W. (1993): Weak compactness in L1(μ,X), Proc. Amer. Math. Soc. 118, no.2, pp.443-453
63. Diestel, J. & Uhl, J. (1977): Vector measures, Math. Surveys vol. 15, Amer. Math. Soc.
64. DiPerna, R.J. and Lions, P.L. (1989): Ordinary differential equations, transport theory and Sobolev spaces, Inventiones Mathematicae, 98, pp.511-547
65. Donchev, T. (2002): Properties of the reachable set of control systems, Systems Control Lett. 46, no.5, pp.379-386
66. Donchev, T. (2002): Properties of one-sided Lipschitz multivalued maps, Nonlinear Analysis, 49, no.1, pp.13-20
67. Donchev, T. (1997): Lower semicontinuous differential inclusions. One-sided Lipschitz approach, Colloq. Math. 74, no.2, pp.177-184
68. Donchev, T. & Dontchev, A.L. (2008): Extensions of Clarke's proximal characterization for reachable mappings of differential inclusions, J. Math. Anal. Appl. 348, no.1, pp.454-460
69. Donchev, T. & Farkhi, E. (1998): Stability and Euler approximations of one-sided Lipschitz differential inclusions, SIAM J. Control Optimization 36, no.2, pp.780-796
70. Dong, G.C. (1991): Nonlinear Partial Differential Equations of Second Order, AMS Translations of Mathematical Monographs 95
71. Doyen, L. (1995): Mutational equations for shapes and vision-based control, J.Math. Imaging Vis. 5, no.2, pp.99-109
72. Doyen, L. (1994): Inverse function theorems and shape optimization, SIAM J. Control Optimization 32, no.6, pp.1621-1642
73. Doyen, L. (1994): Shape Lyapunov functions and stabilization of reachable tubes of control problems. J. Math. Anal. Appl. 184, no.2, pp.222-228
74. Doyen, L. (1993): Filippov and invariance theorems for mutational inclusions of tubes, Set- Valued Anal. 1, no.3, pp.289-303
75. Effros, E.G. & Kazdan, J.L. (1971): On the Dirichlet problem for the heat equation, Indiana Univ. Math. J. 20, no.8, pp.683-693
76. Engel, K.-J. & Nagel, R. (2000): One-Parameter Semigroups of Linear Evolution Equations, Springer
77. Evans, L.C. & Gariepy, R.F. (1992): Measure theory and fine properties of functions, CRC Press
78. Federer, H. (1969): Geometric Measure Theory, Springer
79. Federer, H. (1959): Curvature measures, Trans. Am. Math. Soc. 93, pp.418-491
80. Frankowska, H. (2002): Value function in optimal control, in: Agrachev, A. A. (ed.), Mathematical control theory, ICTP Lect. Notes. 8, pp.515-653
81. Frankowska, H. (1989): Optimal trajectories associated with a solution of the contingent Hamilton-Jacobi equation, Appl. Math. Optimization 19, no.3, pp.291-311
82. Frankowska, H. (1989): Contingent cones to reachable sets of control systems, SIAM J. Control Optimization 27, no.1, pp.170-198
83. Frankowska, H., Plaskacz, S. & Rzeżuchowski, T. (1995): Measurable viability theorems and the Hamilton-Jacobi-Bellman equation, J. Differ. Equations 116, no.2, pp.265-305
84. Fremlin, D.H. (1980/1981): Measurable functions and almost continuous functions. Manuscripta Math. 33, no.3-4, pp.387-405
85. Friedman, A. (1975): Stochastic differential equations and applications, Vol.1, Academic Press
86. Gautier, S. & Pichard, K. (2003): Viability results for mutational equations with delay, Numer. Funct. Anal. Optimiz. 24, no.3 & 4, pp.273-284
87. Gilbarg, D. & Trudinger, N.S. (1983): Elliptic partial differential equations of second order, second edition, Springer
88. Green, J.W. & Valentine, F.A. (1960/1961): On the Arzela-Ascoli theorem, Math. Mag. 34, pp.199-202
89. Gorre, A. (1997): Evolutions of tubes under operability constraints. J. Math. Anal. Appl. 216, no.1, pp.1-22
90. Gorre, A. (1996): Evolution de Tubes Oṕerables gouverńee par des ́equations mutationnelles, Th̀ese de l'Universit́e de Paris-Dauphine
91. Gwiazda, P., Lorenz, Th. & Marciniak-Czochra, A. (2010): A nonlinear structured population model: Lipschitz continuity of measure-valued solutions with respect to model ingredients, to appear in Journal of Differential Equations
92. Hartman, Ph. (1964): Ordinary Differential Equations, Wiley
93. Hirsch, M.W., Smale, St. & Devaney R.L. (2004): Differential Equations, Dynamical Systems, and an Introduction to Chaos (second edition), Elsevier
94. Iannelli, M. (1995): Mathematical Theory of Age-Structured Population Dynamics, Applied Math. Monographs, CNR
95. J̈ahne, B. (2005): Digital image processing (sixth edition), Springer
96. Jarnik, J. & Kurzweil, J. (1977): On conditions on right hand sides of differential relations, Ċasopis Pěst. Mat. 102, pp.334-349
97. Karatzas, I. & Shreve, St.E. (1991): Brownian motion and stochastic calculus (second edition), Springer
98. Kass, M., Witkin, A. & Terzopoulos, D. (1987): Snakes, active contour models, ICCV 1987, pp.259-268
99. Kelley, J.L, (1955): General topology, Van Nostrand, reprinted by Springer
100. Kisielewicz, M. (2001): Weak compactness of solution sets to stochastic differential inclusions with convex right-hand sides, Topol. Methods Nonlinear Anal. 18, no.1, pp.149-169
101. Kisielewicz, M. (1997): Set-valued stochastic integrals and stochastic inclusions, Stochastic Anal. Appl. 15, no.5, pp.783-800
102. Kisielewicz, M. (1992): Weak compactness in spaces C(S,X), in: Information theory, statistical decision functions, random processes, Trans. 11th Prague Conf., Prague/Czech. 1990, Vol.B, pp.101-106 (1992)
103. Kisielewicz, M. (1982): Multivalued differential equations in separable Banach spaces, J. Optimization Theory Appl. 37, pp.231-249
104. Kisielewicz, M., Michta, M. & Motyl, J. (2003): Set valued approach to stochastic control I & II, Dynam. Systems Appl. 12, no.3-4, pp.405-466
105. Kloeden, P.E. & Lorenz, Th. (2010): Stochastic differential equations with nonlocal sample dependence, to appear in Stoch. Anal. Appl.
106. Kloeden, P.E. & Platen, E. (1992): Numerical solution of stochastic differential equations, Springer
107. Kloeden, P.E., Real, J. & Sun, Ch. (2009): Pullback attractors for a semilinear heat equation on time-varying domains, J. Differ. Equations, in press
108. Kloeden, P.E., Sadovsky, B.N. & Vasilyeva, I.E. (2002): Quasi-flows and equations with nonlinear differentials, Nonlinear Anal. 51, no.7, pp.1143-1158
109. Kuratowski, K. & Ryll-Nardzewski, Cz. (1965): A general theorem on selectors, Bull. Acad. Pol. Sci., Śer. Sci. Math. Astron. Phys. 13, pp.397-403
110. Kurzhanskij, A.B. & Filippova, T.F. (1989): On the set-valued calculus in problems of viability and control for dynamic processes: The evolution equation, Ann. Inst. Henri Poincaŕe, Anal. Non Lińeaire 6, Suppl., pp.339-363
111. Ladyzhenskaya, O.A. (1985): The boundary value problems of mathematical physics, Springer
112. Ladyzhenskaya, O.A., Solonnikov, V.A. & Ural'tseva, N.N. (1968): Linear and quasi-linear equations of parabolic type, Translations of Mathematical Monographs 23, American Mathematical Society (AMS)
113. Lakshmikantham, V. & Nieto, J.J. (2003): Differential equations in metric spaces: An introduction and an application to fuzzy differential equations, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. 10, no.6, pp.991-1000
114. Lieberman, G. (1996): Second order parabolic differential equations, World Scientific Publishing
115. Lieberman, G. (1989): Intermediate Schauder theory for second order parabolic equations. III. The tusk conditions, Appl. Anal. 33, no.1-2, pp.25-43
116. Límaco, J., Medeiros, L.A. & Zuazua, E. (2002): Existence, uniqueness and controllability for parabolic equations in non-cylindrical domains, Mat. Contemp. 23, pp.49-70
117. Lorenz, Th. (2009): Mutational Analysis. A joint framework for dynamical systems in and beyond vector spaces, Habilitationsschrift (i.e. thesis for a postdoctoral lecture qualification), Ruprecht-Karls-University of Heidelberg
118. Lorenz, Th. (2009): Mutational inclusions: Differential inclusions in metric spaces, to appear in Discrete Contin. Dyn. Syst. Ser. B
119. Lorenz, Th. (2009): Nonlocal stochastic differential equations: Existence and uniqueness of solutions, to appear in Bol. Soc. Esp. Mat. Apl.
120. Lorenz, Th. (2008): Generalizing mutational equations for uniqueness of some nonlocal 1storder geometric evolutions, Set-Valued Anal. 16, pp.1-50
121. Lorenz, Th. (2008): Shape evolutions under state constraints: A viability theorem, J. Math. Anal. Appl. 340, pp.1204-1225
122. Lorenz, Th. (2008): A viability theorem for morphological inclusions, SIAM J. Control Optim. 47, no.3, pp.1591-1614
123. Lorenz, Th. (2008): Epi-Lipschitzian reachable sets of differential inclusions, System Control Letters 57, pp.703-707
124. Lorenz, Th. (2008): Evolution equations in ostensible metric spaces: First-order evolutions of nonsmooth sets with nonlocal terms, Discuss. Math., Differ. Incl. Control Optim. 28, pp.15-73
125. Lorenz, Th. (2008): Control problems for nonlocal set evolutions, submitted Preprint available at http://www.ub.uni-heidelberg.de/archiv/8022
126. Lorenz, Th. (2007): Radon measures solving the Cauchy problem of the nonlinear transport equation, Preprint available at http://www.ub.uni- heidelberg.de/archiv/7252
127. Lorenz, Th. (2006): Reynold's transport theorem for differential inclusions, Set-Valued Anal. 14, no.3, pp.209-247
128. Lorenz, Th. (2005): Boundary regularity of reachable sets of control systems, Syst. Control Lett. 54, no.9, pp.919-924
129. Lorenz, Th. (2005): Quasilinear continuity equations of measures for bounded BV vector fields, Preprint available at http://www.ub.uni-heidelberg.de/ archiv/5993
130. Lorenz, Th. (2004): First-order geometric evolutions and semilinear evolution equations : A common mutational approach. Doctor thesis (PhD), Ruprecht-Karls-University of Heidelberg, 2004, http://www.ub.uni-heidelberg.de/ archiv/4949
131. Lorenz, Th. (2001): Set-valued maps for image segmentation, Comput. Vis. Sci. 4, no.1, pp.41-57
132. Lumer, G. & Schnaubelt, R. (2001): Time-dependent parabolic problems on non-cylindrical domains with inhomogeneous boundary conditions. Dedicated to Ralph S. Phillips, J. Evol. Equ. 1, no.3, pp.291-309
133. Lumer, G. & Schnaubelt, R. (1999): Local operator methods and time dependent parabolic equations on non-cylindrical domains, in: Demuth,M. et al. (eds.), Evolution equations, Feshbach resonances, singular Hodge theory, Math. Top. 16, Wiley, pp.58-130
134. Maniglia, St. (2007): Probabilistic representation and uniqueness results for measure-valued solutions of transport equations, J. Math. Pures Appl. (9) 87, no.6, pp.601-626
135. Mao, Xuerong (2008): Stochastic differential equations and applications, second edition, Horwood Publishing Limited
136. Matheron, G. (1975): Radom Sets and Integral Geometry, Wiley
137. Metz J.A.J. and Diekmann O. (1986): The Dynamics of Physiologically Structured Populations, Springer, Lecture Notes in Biomathematics, vol.68
138. Michael, E. (1956): Continuous selections I, Annals of Math. 63, pp.361-381
139. Michta, M. (2003): On solutions to stochastic differential inclusions, Discrete Contin. Dyn. Syst. 2003, suppl., pp.618-622
140. Michta, M. (2002): Optimal solutions to stochastic differential inclusions, Appl. Math. (Warsaw) 29, no.4, pp.387-398
141. Molchanov, I. (2005): Theory of Random Sets, Springer
142. Motyl, J. (2000): Viable solutions of set-valued stochastic equation, Optimization 48, no.2, pp.157-176
143. Motyl, J. (1995): On the solution of stochastic differential inclusion, J. Math. Anal. Appl. 192, no.1, pp.117-132
144. Murillo Herńandez, J.A. (2006): Tangential regularity in the space of directionalmorphological transitions, J. Convex Anal. 13, no.2, pp.423-441
145. Nagumo, M. (1942): ̈Uber die Lage der Integralkurven geẅohnlicher Differentialgleichungen, Proc. Phys.-Math. Soc. Japan, III. Ser. 24, pp.551-559
146. Nieto, J.J. & Rodríguez-Ĺopez, R. (2006): Hybrid metric dynamical systems with impulses, Nonlinear Anal. 64, no.2, pp.368-380
147. Øksendal B. (2003): Stochastic differential equations. An introduction with applications (sixth edition), Springer
148. Osher, St. & Fedkiw, R. (2003): Level set methods and dynamic implicit surfaces, Springer
149. Osher, St. & Sethian, J.A. (1988): Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations, J. Comput. Phys. 79, no.1, pp.12-49
150. Panasyuk, A.I. (1995): Quasidifferential equations in a complete metric space under conditions of the Carath́eodory type. I, Differ. Equations 31, no.6, pp.901-910
151. Panasyuk, A.I. (1992): Properties of solutions of a quasidifferential approximation equation and the equation of an integral funnel, Differ. Equations 28, no.9, pp.1259-1266
152. Panasyuk, A.I. (1990): Equations of attainable set dynamics, part 1: Integral funnel equations, J. Optimization Theory Appl. 64, no.2, pp.349-366
153. Panasyuk, A.I (1985): Quasidifferential equations in metric spaces, Differ. Equations 21, pp.914-921
154. Pazy, A. (1983): Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer
155. Perona, P. & Malik, J. (1990): Scale-space and edge detection using anisotropic diffusion, IEEE Trans. Pattern Anal. Mach. Intel. 12, no.7, pp.629-639
156. Perona, P. & Malik, J. (1987): Scale space and edge detection using anisotropic diffusion, in: Proc. of the IEEE Computer Society Workshop on Computer Vision, Miami, FL, pp.16-27
157. Perthame, B. (2007): Transport equations in biology. Birkḧauser
158. Pichard, K. & Gautier, S. (2000): Equations with delay in metric spaces: The mutational approach, Numer. Funct. Anal. Optimiz. 21, no.7 & 8, pp.917-932
159. Poliquin, R.A., Rockafellar, R.T & Thibault, L. (2000): Local differentiability of distance functions, Trans. Am. Math. Soc. 352, no.11, pp.5231-5249
160. Ricceri, B. & Villani, A. (1983): Separability and Scorza-Dragoni's property, Le Matematiche, 37, no.1, pp.156-161
161. Rockafellar, R.T. (1979): Clarke's tangent cones and the boundaries of closed sets in Rn, Nonlinear Anal. Theor. Meth. Appl. 3, pp.145-154
162. Rockafellar, R.T. & Wets, R. (1998): Variational Analysis, Springer
163. Royden, H.L. (1988): Comparison theorems for the matrix Riccati equation, Commun. Pure Appl. Math. 41, no.5, pp.739-746
164. Rzeżuchowski, T. (1999): Continuous parameterization of attainable sets by solutions of differential inclusions, Set-Valued Anal. 7, pp.347-355
165. Rzeżuchowski, T. (1997): Boundary solutions of differential inclusions and recovering the initial data, Set-Valued Anal. 5, pp.181-193
166. Rzeżuchowski, T. (1979): On the set where all the solutions satisfy a differential inclusion, in: Qualitative theory of differential equations, Vol.II, Szeged 1979, Colloq.Math. Soc. J́anos Bolyai 30 (1981), pp.903-913
167. Scorza-Dragoni, G. (1948): Un teorema sulle funzioni continue rispetto ad una e misurabili rispetto ad un'altra variabile, Rend. Semin. Mat. Univ. Padova, 17, pp.102-108
168. Schaefer, H.H. (1971): Topological vector spaces, third printing corrected, Springer
169. Schwartz, L. (1973): Radon measures, Oxford University Press
170. Searćoid, M. (2007): Metric Spaces, Springer
171. Serra, J. (1982): Image Analysis and Mathematical Morphology, Academic Press
172. Sethian, J.A. (1999): Level Set Methods and Fast Marching Methods, second edition, Cambridge University Press
173. Smirnov, V. I. (1953): A Course in Higher Mathematics. Vol.4
174. Sokolowski, J. & Zoĺesio, J.-P. (1992): Introduction to Shape Optimization. Shape Sensitivity Analysis, Springer
175. Souganidis, P.E. (1997): Front propagation: theory and applications, in: Capuzzo Dolcetta, I.at al. (eds.), Viscosity solutions and applications Springer Lecture Notes in Math. 1660, pp.186-242
176. Stassinopoulos, G. & Vinter, R. (1979): Continuous dependence of solutions of a differential inclusion on the right hand side with applications to stability of optimal control problems, SIAM J. Control Optim. 17, no.3, pp.432-449
177. Tolstonogov, A.A. (1983): Equation of the solution funnel of a differential inclusion, Math. Notes 32, pp.908-914
178. Truong-Van, B. & Truong, Xuan Duc Ha (1999): Existence results for viability problem associated to nonconvex stochastic differentiable inclusions, Stochastic Anal. Appl. 17, no.4, pp.667-685
179. Ü lger, A. (1991): Weak compactness in L1(μ,X), Proc. Amer. Math. Soc. 113, no.1, pp.143-149
180. Vinter, R. (2000): Optimal Control, Birkḧauser
181. Walter, W. (2000): Geẅohnliche Differentialgleichungen (seventh edition), Springer
182. Webb, G.F. (1985): Nonlinear Age-Dependent Population Dynamics, Dekker
183. Weickert, J. (1998): Anisotropic diffusion in image processing, Teubner
184. Werner, D. (2002): Funktionalanalysis (4th edition), Springer
185. Williams, D.J. & Shah, M. (1992): A Fast Algorithm for Active Contours and Curvature Estimation, CVGIP : Image Understanding, 55, no.1, pp.14-26
186. Wolenski, P.R. & Zhuang, Yu (1998): Proximal analysis and the minimal time function, SIAM J. Control Optimization 36, no.3, pp.1048-1072
187. Xu, Daoyi, Yang, Zhigua & Huang, Yumei (2008): Existence-uniqueness and continuation theorems for stochastic functional differential equations, J. Differential Equations, 245, pp.1681-1703
188. Yosida, K. (1978): Functional Analysis (fifth edition), Springer, Grundlehren der mathematischen Wissenschaften 123
189. Ziemer, W. (1989): Weakly Differentiable Functions, Springer
190. Zoĺesio, J.-P. (1979): Identification de domaine par d́eformations. Th̀ese de doctorat d'́etat, Universit́e de Nice