Nonexistence results for a higher-order evolution equation with an inhomogeneous term depending on time and space

TL;DR

This paper establishes criteria for the nonexistence of solutions to a higher-order evolution equation with inhomogeneous terms, deriving critical exponents related to space-dependent inhomogeneity.

Contribution

It introduces a general nonexistence criterion and identifies critical exponents for space-dependent inhomogeneous terms in higher-order evolution equations.

Findings

Derived a general nonexistence criterion for weak solutions.

Identified the first Fujita-type critical exponent.

Determined the second Lee-Ni critical exponent.

Abstract

We consider a higher-order evolution equation with an inhomogeneous term depending on time and space. We first derive a general criterion for the nonexistence of weak solutions. Next, we study the particular case when the inhomogeneity depends only on space. In that case, we obtain the first critical exponent in the sense of Fujita, as well as the second critical exponent in the sense of Lee and Ni.