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Mohsen Alimohammady

Academic rank: Professor
ORCID:
Education: PhD.
ScopusId:
Faculty: Faculty of Mathematical Sciences
Address:
Phone: 011-35302462

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 Proceedings of the Indian Academy of Sciences: Mathematical Sciences
DOI
Researchers Mohsen Alimohammady ، Morteza Koozehgar

Abstract

This paper is concerned with the study of nonlinear viscoelastic evolution equation with strong damping and source terms, described by utt − Bu +  t 0 g(t − τ)Bu(τ )dτ + f (x)ut |ut |m−2 = h(x)|u|p−2u, x ∈ int B, t > 0, where B is a stretched manifold. First, we prove the solutions of problem (1.1) in the cone Sobolev space H1, n 2 2,0 (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.