Nonexistence of global weak solutions for evolution equations with fractional Laplacian

TL;DR

This paper proves that certain nonlocal nonlinear parabolic equations involving fractional Laplacians do not admit nontrivial global weak solutions, using the test function method.

Contribution

It establishes the nonexistence of global weak solutions for a class of evolution equations with fractional Laplacian, advancing understanding of their solution behavior.

Findings

No nontrivial global weak solutions exist for the studied equations.

The test function method effectively demonstrates nonexistence.

Results contribute to the theory of fractional Laplacian evolution equations.

Abstract

In this paper, we are interested to analyze a nonlocal nonlinear parabolic equation with fractional Laplacian. We show that there are no nontrivial global weak solutions using the test function method.