Invariance Solutions and Blow-Up Property for Edge Degenerate Pseudo-Hyperbolic Equations in Edge Sobolev Spaces

Carlo Cattani () and Morteza Koozehgar Kalleji ()
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Carlo Cattani: University of Tuscia
Morteza Koozehgar Kalleji: Arak University

A chapter in Nonlinear Analysis, Differential Equations, and Applications, 2021, pp 39-70 from Springer

Abstract: Abstract This article is dedicated to study of the initial-boundary value problem of edge pseudo-hyperbolic system with damping term on the manifold with edge singularity. First, we will discuss about the invariance of solution set of a class of edge degenerate pseudo-hyperbolic equations on the edge Sobolev spaces. Then, by using a family of modified potential wells and concavity methods, it is obtained existence and nonexistence results of global solutions with exponential decay and is shown the blow-up in finite time of solutions on the manifold with edge singularities.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-030-72563-1_3

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DOI: 10.1007/978-3-030-72563-1_3

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