Nonexistence of Global Positive Solutions for p-Laplacian Equations with Non-Linear Memory

Mokhtar Kirane,Ahmad Z Fino,Sebti Kerbal

doi:10.3390/fractalfract5040189

Abstract

The Cauchy problem in Rd,d≥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.

Highlights

In this paper, we consider the following problem: Citation: Kirane, M.; Fino, A.Z.; Kerbal, S
We are interested in the nonexistence of nontrivial global weak solutions
The study of nonexistence of global solutions for nonlinear parabolic equations was started by Fujita [1]; he studied the Cauchy problem ut − ∆u = u, p > 1, t > 0, x ∈ Rd, (2)

Summary

Introduction

We consider the following problem: Citation: Kirane, M.; Fino, A.Z.; Kerbal, S. Mitidieri and Pohozaev [7] completed the study by proving the nonexistence of nontrivial global solution in the case q ≤ q∗ and for all p > 2d/(d +. The test function method was used to prove the nonexistence of global solutions. This method was introduced by Baras and Kersner in [10] and developed by Zhang in [11] and Pohozaev and Mitidieri in [7], it was used by Kirane et al in [12]. We are concerned with the non-existence of nontrivial global solutions of (1); inspired by [7], we choose a suitable test function in the weak formulation of the problem.

Preliminaries

Global Nonexistence