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A note on the existence of global solutions for reaction-diffusion equations with almost-monotonic nonlinearities

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  • We show existence and uniqueness of global solutions for reaction-diffusion equations with almost-monotonic nonlinear terms in $L^q(\Omega)$ for each $1\leq q < \infty$. In particular, we do not assume restriction on the growth of the nonlinearites required by the standar local existence theory.
    Mathematics Subject Classification: Primary: 35A01, 35B33, 35D35, 35K57, 35K20; Secondary: 35B40, 35B41.


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  • [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.


    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.


    H. Brezis and T. Cazenave, A nonlinear heat equation with singular initial data, J. Anal. Math., 68 (1996), 277-304.doi: 10.1007/BF02790212.


    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.


    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.


    D. Henry, "Geometric Theory of Semilinear Parabolic Equations,'' Volume 840 of Lecture Notes in Mathematics, Springer-Verlag, Berlin, 1981.


    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.


    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.


    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.


    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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