On the critical exponents for a fractional diffusion-wave equation with a nonlinear memory term in a bounded domain
Analysis of PDEs
2022-11-04 v2
Abstract
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 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.
Keywords
Cite
@article{arxiv.2211.00308,
title = {On the critical exponents for a fractional diffusion-wave equation with a nonlinear memory term in a bounded domain},
author = {Quanguo Zhang},
journal= {arXiv preprint arXiv:2211.00308},
year = {2022}
}
Comments
24 pages