`a`
Communications on Pure and Applied Analysis (CPAA)
 

A note on the existence of global solutions for reaction-diffusion equations with almost-monotonic nonlinearities
Pages: 635 - 644, Issue 2, March 2014

doi:10.3934/cpaa.2014.13.635      Abstract        References        Full text (355.3K)           Related Articles

Aníbal Rodríguez-Bernal - Departamento de Matemática Aplicada, Universidad Complutense de Madrid, Madrid 28040, Spain (email)
Alejandro Vidal-López - Mathematics Institute, University of Warwick, Coventry, CV4 7AL, United Kingdom (email)

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.
2 J. M. Ball, Strongly continuous semigroups, weak solutions, and the variation of constants formula, Proc. Amer. Math. Soc., 63 (1977), 370-373.
3 H. Brezis and T. Cazenave, A nonlinear heat equation with singular initial data, J. Anal. Math., 68 (1996), 277-304.
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.
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.
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.
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.
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.
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.

Go to top