Three tupes of self-similar blow-up for the fourth-order p-Laplacian equaiton with source: variational and branching approaches

TL;DR

This paper investigates three types of self-similar blow-up in a fourth-order p-Laplacian reaction-diffusion equation, using variational and branching methods to construct and extend blow-up solutions.

Contribution

It introduces a variational framework for regional blow-up solutions and extends these solutions to non-variational cases through a branching approach.

Findings

Identified three distinct blow-up types in the equation.

Constructed self-similar blow-up patterns for regional blow-up.

Extended solutions to non-variational problems using branching methods.

Abstract

The fourth-order quasilinear reaction-diffusion equation with a p-Laplacian operator is shown to admit three types of blow-up. Self-similar patterns are first constructed for the regional blow-up case, where the rescaled problem admits a variational setting. Next, these were extended via a branching approach to non-variational problems.