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Morteza Koozehgar Kalleji

Morteza Koozehgar Kalleji

Academic rank: Assistant Professor
ORCID: https://orcid.org/0000-0002-7052-7241
Education: PhD.
ScopusId: 55803631900
Faculty: Science
Address: Arak University
Phone:

Research

Title
Blow up property for viscoelastic evolution equations on manifolds with conical degeneration
Type
JournalPaper
Keywords
Viscoelastic equation, blow up, Cone Sobolev spaces degenerated differential Operator
Year
2020
Journal Proceeding-mathematical sciences
DOI
Researchers mohsen Alimohammady ، Morteza Koozehgar Kalleji

Abstract

This paper is concerned with the study of the nonlinear viscoelastic evolution equation with strong damping and source terms, described by \[u_{tt} - \Delta_{\mathbb{B}}u + \int_{0}^{t}g(t-\tau)\Delta_{\mathbb{B}}u(\tau)d\tau + f(x)u_{t}|u_{t}|^{m-2} = h(x)|u|^{p-2}u , \hspace{1 cm} x\in int~\mathbb{B}, t > 0,\] where $\mathbb{B}$ is a stretched manifold. First, we prove the solutions of the problem {1.1} in the cone Sobolev space $\mathcal{H}^{1,\frac{n}{2}}_{2,0}(\mathbb{B}),$ which admit a blow up in finite time for $p > m$ and positive initial energy. Then, we construct a lower bound for obtaining blow up time under appropriate assumptions on data.