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Title
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Invariance and existence analysis for semilinear hyperbolic equations with damping and conical singularity
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Type
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JournalPaper
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Keywords
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Semilinear hyperbolic equation, Potential wells, Cone Sobolev spaces, Partial differential operator
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Abstract
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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
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Researchers
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Morteza Koozehgar (Third Researcher), Carlo Cattani (Second Researcher), Mohsen Alimohammady (First Researcher)
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