Generalized convexity and the existence of finite time blow-up solutions for an evolutionary problem

TL;DR

This paper investigates a class of nonlinear nonlocal parabolic equations involving the p-Laplacian with Neumann-Robin boundary conditions, demonstrating conditions under which solutions blow up in finite time.

Contribution

It introduces a new class of nonlinearities for which finite time blow-up solutions exist in nonlocal parabolic equations with boundary conditions.

Findings

Identification of nonlinearities leading to finite time blow-up

Analysis of the influence of boundary conditions on solution behavior

Conditions under which blow-up occurs in the studied equations

Abstract

In this paper we study a class of nonlinearities for which a nonlocal parabolic equation with Neumann-Robin boundary conditions, for $p$-Laplacian, has finite time blow-up solutions.