Dynamics of Partial Differential Equations

Volume 13 (2016)

Number 4

Well posedness and asymptotic behavior of supercritical reaction-diffusion equations with nonlinear boundary conditions

Pages: 273 – 295

DOI: https://dx.doi.org/10.4310/DPDE.2016.v13.n4.a1

Authors

Aníbal Rodríguez-Bernal (Departamento de Matemática Aplicada, and Instituto de Ciencias Matemática, Universidad Complutense de Madrid, Spain)

Alejandro Vidal-López (Department of Mathematical Sciences, Xi’an Jiaotong-Liverpool University, Suzhou, China)

Abstract

We construct solutions of nonlinear reaction-diffusion equations with nonlinear boundary conditions in spaces where the problem is supercritical and show the nonlinear balance required between the nonlinear terms in order to obtain a dissipative system. Assuming this balance, the dynamics of the solutions is the same that takes place in subcritical spaces since their attractors coincide.

Keywords

local existence, nonlinear balance

2010 Mathematics Subject Classification

35B40, 35B41, 35K57, 35K61

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Published 16 December 2016