ON THE CRITICAL EXPONENTS FOR A FRACTIONAL DIFFUSION-WAVE EQUATION WITH A NONLINEAR MEMORY TERM IN A BOUNDED DOMAIN

被引：0

作者：

Zhang, Quan-Guo ^{[1
]}

机构：

[1] Luoyang Normal Univ, Dept Math, Luoyang 471022, Henan, Peoples R China

来源：

TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS | 2024年 / 63卷 / 02期

关键词：

Fractional diffusion-wave equation; blow-up; global existence; nonlinear memory; BLOW-UP SOLUTIONS; CAUCHY-PROBLEMS; WELL-POSEDNESS; GLOBAL EXISTENCE; TIME;

D O I：

10.12775/TMNA.2023.024

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we prove sharp blow-up and global existence results for a time fractional diffusion-wave equation with a nonlinear memory term in a bounded domain, where the fractional derivative in time is taken in the sense of the Caputo type. Moreover, we also give a result for nonexistence of global solutions to a wave equation with a nonlinear memory term in a bounded domain. The proof of blow-up results is based on the eigenfunction method and the asymptotic properties of solutions for an ordinary fractional differential inequality.

引用

页码：455 / 480

页数：26

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