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

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.