Nonexistence of solutions for the quasilinear parabolic differential inequalities with singular potential term and nonlocal source

Suping Xiao,Zhong Bo Fang

doi:10.1186/s13660-020-02329-5

Abstract

This paper is devoted to proving some new nonexistence theorems for a class of quasilinear parabolic differential inequalities with a singular potential term and nonlocal source term in the case of homogeneous and non-homogeneous by the test function method.

Highlights

N p β(y)up(y, t) dy uq(x, t), (x, t) ∈ RN × (0, ∞). They obtained the global nonexistence of nontrivial solutions by the test function method
Huang et al [19] studied the global nonexistence of solutions to a time degenerate type evolution problems with nonlocal sources
Considering the above works, one can find that the study on the nonexistence of solutions for the homogeneous and non-homogeneous quasilinear differential inequalities with a singular potential term and a weighted nonlocal source term has not been started yet

Summary

Introduction

1 Introduction In this paper, we consider the homogeneous and non-homogeneous inequalities with singular potential and weight nonlocal source term of the form ut ≥ In 1966, Fujita [4] studied the following Cauchy problem of the semilinear heat equation with a local source term: ut = u + up, (x, t) ∈ RN × (0, ∞), and obtained the critical exponent qc = 1 + On the existence versus nonexistence of nonnegative nontrivial global solution.

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Results

Conclusion