Optimal control of nonlinear diffusion equations with rough initial data

Journal of the Franklin Institute

Volumn 337, Issue 6, 2000, Pages 673-690

  Rubio, J E ^a  

^a UNIVERSITY OF LEEDS   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; CONTROL SYSTEM ANALYSIS; CONTROL SYSTEM SYNTHESIS; LINEAR PROGRAMMING; NONLINEAR CONTROL SYSTEMS; PROBLEM SOLVING; STATE SPACE METHODS;

DELTA FUNCTIONS; NONLINEAR DIFFUSION EQUATIONS;

OPTIMAL CONTROL SYSTEMS;

EID: 0034259389     PISSN: 00160032     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0016-0032(00)00045-4     Document Type: Article

References (34)

1. J.E. Rubio, The global optimization of variational problems with discontinuous solutions, J. Global Optim. 12 (1998) 225-237.
2. J.E. Rubio, Semi-infinite programming and control problems, in: P. Pardalos, C. Floudas (Eds.), Encyclopedia of Optimization, Kluwer, Dordrecht, 2000 (in press).
3. J.E. Rubio, Optimal control problems with unbounded control sets, Optimization, in press.
4. J.E. Rubio, The global control of shock waves, in: M. Oberguggenberger (Ed.), Proceedings of a Conference on Nonlinear Theory of Generalized Functions, Vienna, 1997, Research Notes in Mathematics, 401, Chapman & Hall, London, 1999.
5. J.E. Rubio, The global control of shock waves, Technical Report 532, The Erwin Schrödinger International Institute for Mathematical Physics, 1998.
6. J.E. Rubio, Optimization and Nonstandard Analysis, Marcel Dekker, New York, 1994.
7. J.E. Rubio, The global control of nonlinear diffusion equations, SIAM J. Control Optim. 33 (1995) 308-322.
8. J.F. Colombeau, M. Langlais, Generalized solutions of nonlinear parabolic equations with distributions as initial conditions, J. Math. Anal. Appl. 145 (1990) 186-196.
9. J.F. Colombeau, A. Heibig, M. Oberguggenberger, Generalized solutions to partial differential equations of evolution type, Acta Appl. Math. 45 (1996) 115-142.
10. M. Oberguggenberger, Multiplication of Distributions and Applications to Partial Differential Equations, Longman, New York, 1992.
11. O. Hernandez-Lerna, J. B. Lasserre, Further Topics on Discrete-Time Markov Control Processes, Springer, Berlin, 1999.
12. J.E. Rubio, Control and Optimisation: The Linear Treatment of Nonlinear Problems, MUP-Wiley, New York, 1986.
13. J.E. Rubio, An existence theorem in the calculus of variations, J. Optim. Theory Appl. 19 (1976) 81-87.
14. A.G. Bhatt, R.L. Karandikar, Invariant measures and evolution equations for markov processes, Ann. Probab. 21 (1993) 2246-2268.
15. V.P. Mikhailov, Partial Differential Equations, Mir, Moscow, 1978.
16. O. Ladyženskaya, Linear and Quasilinear Equations of Parabolic Type, American Mathematical Society, Providence, RI, 1968.
17. W.E. Fitzgibbon, H.F. Walker, Nonlinear Diffusion, Pitman, London, 1977.
18. A. Fakharzadeh, Shapes, measures and elliptic equations, Ph.D. Thesis, University of Leeds, 1997.
19. C. Berge, Topological Spaces, Oliver & Boyd, Edinburgh, 1963.
20. M.E. Monroe, Introduction to Measure and Integration, Addison-Wesley, Reading, MA, 1953.
21. G. Choquet, Lectures on Analysis, Benjamin, New York, 1969.
22. N.J. Cutland (Ed.), Nonstandard Analysis and its Applications, Cambridge University Press, Cambridge, 1988.
23. H. Render, Pushing down Loeb measures, Math. Scand. 72 (1993) 61-84.
24. C.W. Henson, Analytic sets, Baire sets and the standard part map, Canad. J. Math. 31 (1979) 663-672.
25. J.M. Aldaz, A characterization of universal Loeb measurability for completely regular Hausdorff spaces, Canad. J. Math. 44 (1992) 673-690.
26. D. Landers, L. Rogge, Universal Loeb-measurability of sets and of the standard part map with applications, Trans. Amer. Math. Soc. 304 (1987) 229-243.
27. H. Rudolph, Simplexalgorithmus der semiinfiniten linearen Optimierung, Wiss. TH Leuna-Merseburg Tech. Hochsch. 5 (1987) 782-806.
28. H. Rudolph, Global solution in optimal control via silp, In: H.-J. Sebastian (Ed.), System Modelling and Optimization, Lecture Notes in Control and Information Sciences, Vol. 143, Springer, Berlin, 1990, pp. 394-402.
29. E.J. Anderson, A.B. Philpott, Infinite Programming, Springer, Berlin, 1985.
30. K. Glashof, S. Gustafson, Linear Optimization and Approximation, Springer, Berlin, 1983.
31. H. Rudolph, Simplexalgorithmus der semiinfiniten linearen Optimierung, Wiss. TH Leuna-Merseburg Tech. Hochsch. 5 (1987) 782-806.
32. H. Rudolph, Global solution in optimal control via silp, in: H.-J. Sebastian (Ed.), System Modelling and Optimization Lecture Notes in Control and Information Sciences, Vol. 143, Springer, Berlin, 1990, pp. 394-402.
33. K.H. Hoffmann, A. Klostemair, A semiinfinite linear programming procedure and applications to approximation problems in optimal control, in: Approximation Theory II, Academic Press, New York, 1976.
34. J.E. Rubio, The global control of nonlinear diffusion equations, SIAM J. Control Optim. 33 (1995) 308-322.