Dynamics of Partial Differential Equations
Volume 13 (2016)
Well posedness and asymptotic behavior of supercritical reaction-diffusion equations with nonlinear boundary conditions
Pages: 273 – 295
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.
local existence, nonlinear balance
2010 Mathematics Subject Classification
35B40, 35B41, 35K57, 35K61