-
1
-
-
84914830669
-
Lp bounds of solutions of reaction-diffusion equations
-
Alikakos N 1979 Lp bounds of solutions of reaction-diffusion equations Commun. Part. Differ. Equ. 4 827-68
-
(1979)
Commun. Part. Differ. Equ.
, vol.4
, pp. 827-868
-
-
Alikakos, N.1
-
2
-
-
0001742516
-
Dynamic theory of quasilinear parabolic systems: III. Global existence
-
Amann H 1989 Dynamic theory of quasilinear parabolic systems: III. Global existence Meteorol. Z. 202 219-50
-
(1989)
Meteorol. Z.
, vol.202
, pp. 219-250
-
-
Amann, H.1
-
6
-
-
84939975625
-
Continuum thermodynamics of chemically reacting fluid mixtures
-
Bothe D and Dreyer W 2014 Continuum thermodynamics of chemically reacting fluid mixtures Acta Mech. 26 753-69
-
(2014)
Acta Mech.
, vol.26
, pp. 753-769
-
-
Bothe, D.1
Dreyer, W.2
-
7
-
-
84929372398
-
Global existence for a class of reaction-diffusion systems with mass action kinetics and concentration-dependent diffusivities
-
Bothe D and Rolland G 2015 Global existence for a class of reaction-diffusion systems with mass action kinetics and concentration-dependent diffusivities Acta Appl. Math. in press (doi:10.1007/s10440-014-9968-y)
-
(2015)
Acta Appl. Math.
-
-
Bothe, D.1
Rolland, G.2
-
10
-
-
84859075811
-
Nonlinear Poisson-Nernst-Planck equations for ion flux through confined geometries
-
Burger M, Schlake B and Wolfram W-T 2012 Nonlinear Poisson-Nernst-Planck equations for ion flux through confined geometries Nonlinearity 25 961-90
-
(2012)
Nonlinearity
, vol.25
, Issue.4
, pp. 961-990
-
-
Burger, M.1
Schlake, B.2
Wolfram, W.-T.3
-
11
-
-
84899751316
-
Improved duality estimates and applications to reaction-diffusion equations
-
Cañizo J A, Desvillettes L and Fellner K 2014 Improved duality estimates and applications to reaction-diffusion equations Commun. Part. Differ. Equ. 39 1185-204
-
(2014)
Commun. Part. Differ. Equ.
, vol.39
, pp. 1185-1204
-
-
Cañizo, J.A.1
Desvillettes, L.2
Fellner, K.3
-
12
-
-
18044401055
-
Entropy dissipation methods for degenerate parabolic problems and generalized Sobolev inequalities
-
Carrillo J A, Jüngel A, Markowich P, Toscani G and Unterreiter A 2001 Entropy dissipation methods for degenerate parabolic problems and generalized Sobolev inequalities Mon.hefte Math. 133 1-82
-
(2001)
Mon.hefte Math.
, vol.133
, pp. 1-82
-
-
Carrillo, J.A.1
Jüngel, A.2
Markowich, P.3
Toscani, G.4
Unterreiter, A.5
-
15
-
-
14544281036
-
Analysis of a multi-dimensional parabolic population model with strong cross-diffusion
-
Chen L and Jüngel A 2004 Analysis of a multi-dimensional parabolic population model with strong cross-diffusion SIAM J. Math. Anal. 36 301-22
-
(2004)
SIAM J. Math. Anal.
, vol.36
, pp. 301-322
-
-
Chen, L.1
Jüngel, A.2
-
16
-
-
33645922467
-
Analysis of a parabolic cross-diffusion population model without self-diffusion
-
Chen L and Jüngel A 2006 Analysis of a parabolic cross-diffusion population model without self-diffusion J. Differ. Equ. 224 39-59
-
(2006)
J. Differ. Equ.
, vol.224
, pp. 39-59
-
-
Chen, L.1
Jüngel, A.2
-
17
-
-
33847127029
-
Analysis of a parabolic cross-diffusion semiconductor model with electron-hole scattering
-
Chen L and Jüngel A 2007 Analysis of a parabolic cross-diffusion semiconductor model with electron-hole scattering Commun. Part. Differ. Equ. 32 127-48
-
(2007)
Commun. Part. Differ. Equ.
, vol.32
, pp. 127-148
-
-
Chen, L.1
Jüngel, A.2
-
20
-
-
0031280714
-
Symmetrization and entropy inequality for general diffusion equations
-
Degond P, Génieys S and Jüngel A 1997 Symmetrization and entropy inequality for general diffusion equations C. R. Acad. Sci. Paris 325 963-8
-
(1997)
C. R. Acad. Sci. Paris
, vol.325
, pp. 963-968
-
-
Degond, P.1
Génieys, S.2
Jüngel, A.3
-
25
-
-
84929372401
-
New results for triangular reaction cross-diffusion system
-
Desvillettes L and Trescases A 2015 New results for triangular reaction cross-diffusion system J. Math. Anal. Appl. in press (doi:10.1016/j.jmaa.2015.03.078)
-
(2015)
J. Math. Anal. Appl.
-
-
Desvillettes, L.1
Trescases, A.2
-
26
-
-
84856351017
-
Compact families of piecewise constant functions in Lp(0, T; B)
-
Dreher M and Jüngel A 2012 Compact families of piecewise constant functions in Lp(0, T; B) Nonlinear Anal. 75 3072-7
-
(2012)
Nonlinear Anal.
, vol.75
, pp. 3072-3077
-
-
Dreher, M.1
Jüngel, A.2
-
27
-
-
80054097536
-
Parabolic systems with polynomial growth and regularity
-
Duzaar F, Mingione G and Steffen K 2011 Parabolic systems with polynomial growth and regularity Mem. Am. Math. Soc. 214 118
-
(2011)
Mem. Am. Math. Soc.
, vol.214
, Issue.1005
, pp. 118
-
-
Duzaar, F.1
Mingione, G.2
Steffen, K.3
-
28
-
-
84929372402
-
-
Fuhrmann J 2014 Personal communication
-
(2014)
-
-
Fuhrmann, J.1
-
29
-
-
0242389718
-
Semi-discretization in time and numerical convergence of solutions of a nonlinear cross-diffusion population model
-
Galiano G, Garzón M and Jüngel A 2003 Semi-discretization in time and numerical convergence of solutions of a nonlinear cross-diffusion population model Numer. Math. 93 655-73
-
(2003)
Numer. Math.
, vol.93
, pp. 655-673
-
-
Galiano, G.1
Garzón, M.2
Jüngel, A.3
-
30
-
-
0037175732
-
Coupling Poisson-Nernst-Planck and density functional theory to calculate ion flux
-
Gillespie D, Nonner W and Eisenberg R 2002 Coupling Poisson-Nernst-Planck and density functional theory to calculate ion flux J. Phys.: Condens. Matter 14 12129-45
-
(2002)
J. Phys.: Condens. Matter
, vol.14
, Issue.46
, pp. 12129-12145
-
-
Gillespie, D.1
Nonner, W.2
Eisenberg, R.3
-
31
-
-
0001409903
-
Non-uniqueness for a semilinear initial value problem
-
Haraux A and Weissler F 1982 Non-uniqueness for a semilinear initial value problem Indiana Univ. Math. J. 31 167-89
-
(1982)
Indiana Univ. Math. J.
, vol.31
, pp. 167-189
-
-
Haraux, A.1
Weissler, F.2
-
32
-
-
0036846937
-
A mechanical model of tumor encapsulation and transcapsular spread
-
Jackson T and Byrne H 2002 A mechanical model of tumor encapsulation and transcapsular spread Math. Biosci. 180 307-28
-
(2002)
Math. Biosci.
, vol.180
, pp. 307-328
-
-
Jackson, T.1
Byrne, H.2
-
33
-
-
84860377923
-
Entropy structure of a cross-diffusion tumor-growth model
-
Jüngel A and Stelzer I 2012 Entropy structure of a cross-diffusion tumor-growth model Math. Models Meth. Appl. Sci. 22 1250009
-
(2012)
Math. Models Meth. Appl. Sci.
, vol.22
-
-
Jüngel, A.1
Stelzer, I.2
-
34
-
-
84888877408
-
Analysis of Maxwell-Stefan systems for multicomponent mixtures
-
Jüngel A and Stelzer I 2014 Analysis of Maxwell-Stefan systems for multicomponent mixtures SIAM J. Math. Anal. 45 2421-40
-
(2014)
SIAM J. Math. Anal.
, vol.45
, pp. 2421-2440
-
-
Jüngel, A.1
Stelzer, I.2
-
36
-
-
84972554928
-
On the normal form of the symmetric hyperbolic-parabolic systems associated with the conservation laws
-
Kawashima S and Shizuta Y 1988 On the normal form of the symmetric hyperbolic-parabolic systems associated with the conservation laws Tohoku Math. J. II 40 449-64
-
(1988)
Tohoku Math. J.
, vol.40
, Issue.3
, pp. 449-464
-
-
Kawashima, S.1
Shizuta, Y.2
-
37
-
-
0000297309
-
Smooth solutions to a quasi-linear system of diffusion equations for a certain population model
-
Kim J 1984 Smooth solutions to a quasi-linear system of diffusion equations for a certain population model Nonlinear Anal. 8 1121-44
-
(1984)
Nonlinear Anal.
, vol.8
, pp. 1121-1144
-
-
Kim, J.1
-
38
-
-
0009035974
-
Invariant regions for quasilinear reaction-diffusion systems and applications to a two population model
-
Küfner K 1996 Invariant regions for quasilinear reaction-diffusion systems and applications to a two population model NoDEA Nonlinear Differ. Equ. Appl. 3 421-44
-
(1996)
NoDEA Nonlinear Differ. Equ. Appl.
, vol.3
, pp. 421-444
-
-
Küfner, K.1
-
40
-
-
31744452122
-
Global existence for a class of strongly coupled parabolic systems
-
Le D 2006 Global existence for a class of strongly coupled parabolic systems Ann. Math. 185 133-54
-
(2006)
Ann. Math.
, vol.185
, pp. 133-154
-
-
Le, D.1
-
41
-
-
0036054584
-
Cross diffusion systems in n spatial dimensional domains
-
Le D 2002 Cross diffusion systems in n spatial dimensional domains Indiana Univ. Math. J. 51 625-43
-
(2002)
Indiana Univ. Math. J.
, vol.51
, Issue.3
, pp. 625-643
-
-
Le, D.1
-
42
-
-
31744448267
-
Everywhere regularity of solutions to a class of strongly coupled degenerate parabolic systems
-
Le D and Nguyen T 2006 Everywhere regularity of solutions to a class of strongly coupled degenerate parabolic systems Commun. Part. Differ. Equ. 31 307-24
-
(2006)
Commun. Part. Differ. Equ.
, vol.31
, pp. 307-324
-
-
Le, D.1
Nguyen, T.2
-
43
-
-
84861403589
-
Global well-posedness of a conservative relaxed cross diffusion system
-
Lepoutre T, Pierre M and Rolland G 2012 Global well-posedness of a conservative relaxed cross diffusion system SIAM J. Math. Anal. 44 1674-93
-
(2012)
SIAM J. Math. Anal.
, vol.44
, pp. 1674-1693
-
-
Lepoutre, T.1
Pierre, M.2
Rolland, G.3
-
44
-
-
84888105530
-
Gradient structures and geodesic convexity for reaction-diffusion systems
-
Liero M and Mielke A 2005 Gradient structures and geodesic convexity for reaction-diffusion systems Phil. Trans. R. Soc. A 371 20120346
-
(2005)
Phil. Trans. R. Soc.
, vol.371
-
-
Liero, M.1
Mielke, A.2
-
46
-
-
84929372405
-
-
Marion M and Temam R 2013 Global existence for fully nonlinear reaction-diffusion systems describing multicomponent reactive flows (arXiv:1310.2624)
-
(2013)
-
-
Marion, M.1
Temam, R.2
-
48
-
-
2942720712
-
Ionic diffusions through confined geometries: From Langevin equations to partial differential equations
-
Nadler B, Schuss Z, Singer A and Eisenberg R 2004 Ionic diffusions through confined geometries: from Langevin equations to partial differential equations J. Phys.: Condens. Matter 16 S2153
-
(2004)
J. Phys.: Condens. Matter
, vol.16
, Issue.22
, pp. S2153
-
-
Nadler, B.1
Schuss, Z.2
Singer, A.3
Eisenberg, R.4
-
49
-
-
84929315038
-
Macroscopic cross-diffusion models derived from spatially discrete continuous time microscopic models
-
Ostrander S 2011 Macroscopic cross-diffusion models derived from spatially discrete continuous time microscopic models SIAM Undergrad. Res. Online 4 51-71
-
(2011)
SIAM Undergrad. Res. Online
, vol.4
, pp. 51-71
-
-
Ostrander, S.1
-
50
-
-
67651113652
-
Continuous models for cell migration in tissues and applications to cell sorting via differential chemotaxis
-
Painter K 2009 Continuous models for cell migration in tissues and applications to cell sorting via differential chemotaxis Bull. Math. Biol. 71 1117-47
-
(2009)
Bull. Math. Biol.
, vol.71
, pp. 1117-1147
-
-
Painter, K.1
-
51
-
-
4944248574
-
Volume-filling and quorum-sensing in models for chemosensitive movement
-
Painter K and Hillen T 2002 Volume-filling and quorum-sensing in models for chemosensitive movement Can. Appl. Math. Q. 10 501-43
-
(2002)
Can. Appl. Math. Q.
, vol.10
, pp. 501-543
-
-
Painter, K.1
Hillen, T.2
-
52
-
-
0031489813
-
Blowup in reaction-diffusion systems with dissipation of mass
-
Pierre M and Schmitt D 1997 Blowup in reaction-diffusion systems with dissipation of mass SIAM J. Math. Anal. 28 259-69
-
(1997)
SIAM J. Math. Anal.
, vol.28
, pp. 259-269
-
-
Pierre, M.1
Schmitt, D.2
-
53
-
-
27844594320
-
Maximal regularity for evolution equations in Lp-spaces
-
Prüss J 2003 Maximal regularity for evolution equations in Lp-spaces Conf. Semin. Mat. Univ. Bari 285 1-39
-
(2003)
Conf. Semin. Mat. Univ. Bari
, vol.285
, pp. 1-39
-
-
Prüss, J.1
-
54
-
-
0000286193
-
Invariant sets for strongly coupled reaction-diffusion systems under general boundary conditions
-
Redlinger K 1989 Invariant sets for strongly coupled reaction-diffusion systems under general boundary conditions Arch. Ration. Mech. Anal. 108 281-91
-
(1989)
Arch. Ration. Mech. Anal.
, vol.108
, pp. 281-291
-
-
Redlinger, K.1
-
58
-
-
0037057996
-
Uniform boundedness and convergence of solutions to cross-diffusion systems
-
Shim S-A 2002 Uniform boundedness and convergence of solutions to cross-diffusion systems J. Differ. Equ. 185 281-305
-
(2002)
J. Differ. Equ.
, vol.185
, pp. 281-305
-
-
Shim, S.-A.1
-
59
-
-
25644447075
-
Some (new) counterexamples of parabolic systems
-
Stará J and John O 1995 Some (new) counterexamples of parabolic systems Comment. Math. Univ. Carolinae 36 503-10
-
(1995)
Comment. Math. Univ. Carolinae
, vol.36
, pp. 503-510
-
-
Stará, J.1
John, O.2
-
60
-
-
77949560849
-
A density-dependent chemotaxis-haptotaxis system modeling cancer invasion
-
Tao Y and Cui C 2010 A density-dependent chemotaxis-haptotaxis system modeling cancer invasion J. Math. Anal. Appl. 367 612-24
-
(2010)
J. Math. Anal. Appl.
, vol.367
, pp. 612-624
-
-
Tao, Y.1
Cui, C.2
-
63
-
-
79960761054
-
Volume filling effect in modelling chemotaxis
-
Wrzosek D 2010 Volume filling effect in modelling chemotaxis Math. Modelling Nat. Phenom. 5 123-47
-
(2010)
Math. Modelling Nat. Phenom.
, vol.5
, pp. 123-147
-
-
Wrzosek, D.1
-
64
-
-
38248999657
-
Global solution to some quasilinear parabolic systems in population dynamics
-
Yagi A 1993 Global solution to some quasilinear parabolic systems in population dynamics Nonlin. Anal. 21 603-30
-
(1993)
Nonlin. Anal.
, vol.21
, pp. 603-630
-
-
Yagi, A.1
|