Nonexistence of global positive solutions for p-Laplacian equations with non-linear memory

TL;DR

This paper proves that certain p-Laplacian equations with non-linear memory in an unbounded domain do not admit nontrivial global weak solutions, using the test function method.

Contribution

It establishes the nonexistence of global solutions for a class of non-local in time p-Laplacian equations with non-linear memory.

Findings

No nontrivial global weak solutions exist for the considered equations.

The test function method effectively demonstrates nonexistence results.

Results apply to equations in be9d domains with non-local temporal terms.

Abstract

The Cauchy problem in $\mathbb{R}^d,$ $d\geq 1,$ for a non-local in time p-Laplacian equations is considered. The nonexistence of nontrivial global weak solutions by using the test function method is obtained.