English

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}
}

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24 pages