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 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.
Citation
Quan-Guo Zhang. "On the critical exponents for a fractional diffusion-wave equation with a nonlinear memory term in a bounded domain." Topol. Methods Nonlinear Anal. 63 (2) 455 - 480, 2024. https://doi.org/10.12775/TMNA.2023.024
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