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Mohsen Alimohammady

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

Research

Title
Invariance and existence analysis for semilinear hyperbolic equations with damping and conical singularity
Type
JournalPaper
Keywords
Semilinear hyperbolic equation, Potential wells, Cone Sobolev spaces, Partial differential operator
Year
2017
Journal JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
DOI
Researchers Mohsen Alimohammady ، Carlo Cattani ، Morteza Koozehgar

Abstract

In this paper, we will discuss about the invariance of solution set and present the existence and non-existence of the global solutions a class of initial-boundary value problems with dissipative terms is considered for a class of semilinear degenerate hyperbolic equations on the cone Sobolev spaces. First, we will discuss the invariance of some sets corresponding to the problem (1.1) and then, by using a family of potential wells and concavity methods, we obtain existence and non-existence results of global solutions with exponential decay and show the blow-up in finite time of solutions on a manifold with conical singularities