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A note on the existence of global solutions for reaction-diffusion equations with almost-monotonic nonlinearities
1. | Departamento de Matemática Aplicada, Universidad Complutense de Madrid, Madrid 28040 |
2. | Mathematics Institute, University of Warwick, Coventry, CV4 7AL, United Kingdom |
References:
[1] |
J. M. Arrieta, J. W. Cholewa, T. Dlotko and A. Rodríguez-Bernal, Asymptotic behavior and attractors for reaction diffusion equations in unbounded domains, Nonlinear Anal., 56 (2004), 515-554.
doi: 10.1016/j.na.2003.09.023. |
[2] |
J. M. Ball, Strongly continuous semigroups, weak solutions, and the variation of constants formula, Proc. Amer. Math. Soc., 63 (1977), 370-373.
doi: 10.2307/2041821. |
[3] |
H. Brezis and T. Cazenave, A nonlinear heat equation with singular initial data, J. Anal. Math., 68 (1996), 277-304.
doi: 10.1007/BF02790212. |
[4] |
A. Carvalho, J. A. Langa and J. Robinson., "Attractors for Infinite-dimensional Non-autonomous Dynamical Systems,'' volume 182 of Applied Mathematical Sciences, Springer, New York, 2012.
doi: 10.1007/978-1-4614-4581-4_1. |
[5] |
J. W. Cholewa and A. Rodríguez-Bernal, Extremal equilibria for dissipative parabolic equations in locally uniform spaces, Math. Models Methods Appl. Sci., 19 (2009), 1995-2037.
doi: 10.1142/S0218202509004029. |
[6] |
D. Henry, "Geometric Theory of Semilinear Parabolic Equations,'' Volume 840 of Lecture Notes in Mathematics, Springer-Verlag, Berlin, 1981. |
[7] |
M. Marcus and L. Véron, Initial trace of positive solutions of some nonlinear parabolic equations, Comm. Partial Differential Equations, 24 (1999), 1445-1499.
doi: 10.1080/03605309908821471. |
[8] |
J. C. Robinson, A. Rodríguez-Bernal and A. Vidal-López, Pullback attractors and extremal complete trajectories for non-autonomous reaction-diffusion problems, J. Differ. Equations, 238 (2007), 289-337.
doi: 10.1016/j.jde.2007.03.028. |
[9] |
A. Rodríguez-Bernal, Attractors for parabolic equations with nonlinear boundary conditions, critical exponents, and singular initial data, J. Differ. Equations, 181 (2002), 165-196.
doi: 10.1006/jdeq.2001.4072. |
[10] |
A. Rodríguez-Bernal and A. Vidal-López, Extremal equilibria for reaction-diffusion equations in bounded domains and applications, Journal of Differential Equations, 244 (2008), 2983-3030.
doi: 10.1016/j.jde.2008.02.046. |
show all references
References:
[1] |
J. M. Arrieta, J. W. Cholewa, T. Dlotko and A. Rodríguez-Bernal, Asymptotic behavior and attractors for reaction diffusion equations in unbounded domains, Nonlinear Anal., 56 (2004), 515-554.
doi: 10.1016/j.na.2003.09.023. |
[2] |
J. M. Ball, Strongly continuous semigroups, weak solutions, and the variation of constants formula, Proc. Amer. Math. Soc., 63 (1977), 370-373.
doi: 10.2307/2041821. |
[3] |
H. Brezis and T. Cazenave, A nonlinear heat equation with singular initial data, J. Anal. Math., 68 (1996), 277-304.
doi: 10.1007/BF02790212. |
[4] |
A. Carvalho, J. A. Langa and J. Robinson., "Attractors for Infinite-dimensional Non-autonomous Dynamical Systems,'' volume 182 of Applied Mathematical Sciences, Springer, New York, 2012.
doi: 10.1007/978-1-4614-4581-4_1. |
[5] |
J. W. Cholewa and A. Rodríguez-Bernal, Extremal equilibria for dissipative parabolic equations in locally uniform spaces, Math. Models Methods Appl. Sci., 19 (2009), 1995-2037.
doi: 10.1142/S0218202509004029. |
[6] |
D. Henry, "Geometric Theory of Semilinear Parabolic Equations,'' Volume 840 of Lecture Notes in Mathematics, Springer-Verlag, Berlin, 1981. |
[7] |
M. Marcus and L. Véron, Initial trace of positive solutions of some nonlinear parabolic equations, Comm. Partial Differential Equations, 24 (1999), 1445-1499.
doi: 10.1080/03605309908821471. |
[8] |
J. C. Robinson, A. Rodríguez-Bernal and A. Vidal-López, Pullback attractors and extremal complete trajectories for non-autonomous reaction-diffusion problems, J. Differ. Equations, 238 (2007), 289-337.
doi: 10.1016/j.jde.2007.03.028. |
[9] |
A. Rodríguez-Bernal, Attractors for parabolic equations with nonlinear boundary conditions, critical exponents, and singular initial data, J. Differ. Equations, 181 (2002), 165-196.
doi: 10.1006/jdeq.2001.4072. |
[10] |
A. Rodríguez-Bernal and A. Vidal-López, Extremal equilibria for reaction-diffusion equations in bounded domains and applications, Journal of Differential Equations, 244 (2008), 2983-3030.
doi: 10.1016/j.jde.2008.02.046. |
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