Invariance and existence analysis for semilinear hyperbolic equations with damping and conical singularity

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:455

Article

Alimohammady, Mohsen¹  Cattani, Carlo²  Kalleji, Morteza Koozehgar³ 

[1] Univ Mazandaran, Fac Math Sci, Dept Math, Babol Sar 474161468, Iran

[2] Univ Tuscia, Engn Sch, I-01100 Viterbo, Italy

[3] Arak Univ, Dept Math, Fac Sci, Arak 3815688349, Iran

关键词: Semilinear hyperbolic equation;    Potential wells;    Cone Sobolev spaces;    Partial differential operator;   

DOI  :  10.1016/j.jmaa.2017.05.057

来源: Elsevier

【 摘 要 】

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. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free