Nonlinear balance and asymptotic behavior of supercritical reaction-diffusion equations with nonlinear boundary conditions

TL;DR

This paper investigates supercritical reaction-diffusion equations with nonlinear boundary conditions, identifying the nonlinear balance needed for dissipative behavior and demonstrating that, under this balance, the dynamics mirror those in subcritical spaces.

Contribution

It establishes conditions for nonlinear balance in supercritical reaction-diffusion equations, ensuring dissipative dynamics similar to subcritical cases.

Findings

Constructed solutions in supercritical spaces

Identified nonlinear balance for dissipation

Demonstrated dynamics equivalence to subcritical cases

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 take place in subcritical spaces.