On the critical exponents for a fractional diffusion-wave equation with a nonlinear memory term in a bounded domain
DOI:
https://doi.org/10.12775/TMNA.2023.024Słowa kluczowe
Fractional diffusion-wave equation, blow-up, global existence, nonlinear memoryAbstrakt
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.Bibliografia
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