On nonexistence of Baras--Goldstein type for higher-order parabolic equations with singular potentials

TL;DR

This paper extends the nonexistence results for heat equations with singular potentials to higher-order parabolic equations, demonstrating that solutions do not exist under certain supercritical conditions.

Contribution

It provides the first nonexistence proof for higher-order parabolic equations with Hardy-supercritical singular potentials, generalizing previous results for second-order heat equations.

Findings

Nonexistence of solutions for higher-order equations with supercritical singular potentials

Extension of classical results to more complex PDEs

Discussion of implications for nonlinear singular PDEs

Abstract

An analogy of nonexistence result by Baras and Goldstein (1984), for the heat equation with inverse singular potential, is proved for 2mth-order linear parabolic equations with Hardy-supercritical singular potentials. Extensions to other linear and nonlinear singular PDEs are discussed.