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Blow-up analysis of a nonlinear pseudo-parabolic equation with memory term
- Source :
- AIMS Mathematics, Vol 5, Iss 4, Pp 3408-3422 (2020)
- Publication Year :
- 2020
- Publisher :
- AIMS Press, 2020.
-
Abstract
- This paper deals with the blow-up phenomena for a nonlinear pseudo-parabolic equation with a memory term $u_{t}-\triangle{u}-\triangle{u}_{t}+\int_{0}^{t}g(t-\tau)\triangle{u}(\tau)d\tau=|{u}|^{p}{u}$ in a bounded domain, with the initial and Dirichlet boundary conditions. We first obtain the finite time blow-up results for the solutions with initial data at non-positive energy level as well as arbitrary positive energy level, and give some upper bounds for the blow-up time $T^{*}$ depending on the sign and size of initial energy $E(0)$. In addition, a lower bound for the life span $T^{*}$ is derived by means of a differential inequality technique if blow-up does occur.
Details
- Language :
- English
- ISSN :
- 24736988
- Volume :
- 5
- Issue :
- 4
- Database :
- Directory of Open Access Journals
- Journal :
- AIMS Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.95b1532dd0d7485aa4bebdf5f23265de
- Document Type :
- article
- Full Text :
- https://doi.org/10.3934/math.2020220/fulltext.html