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Existence and nonexistence of global solutions of some system of semilinear wave equations

✍ Scribed by Meng-Rong Li; Long-Yi Tsai

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
213 KB
Volume
54
Category
Article
ISSN
0362-546X

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✦ Synopsis

An initial boundary value problem for systems of semilinear wave equations in a bounded domain is considered. We prove the global existence, uniqueness and blow-up of solutions by energy methods and give some estimates for the lifespan of solutions.

πŸ“œ SIMILAR VOLUMES

Global nonexistence of solutions to a se
Global nonexistence of solutions to a semilinear wave equation in the Minkowski space
✍ Xuefei Liu; Yong Zhou πŸ“‚ Article πŸ“… 2008 πŸ› Elsevier Science 🌐 English βš– 209 KB

This work presents the finite-time blow-up of solutions to the equation in the Minkowski space. We extend the previous result of Belchev, Kepka and Zhou [E. Belchev, M. Kepka, Z. Zhou, Finite-time blow-up of solutions to semilinear wave equations, J. Funct. Anal. 190 (1) (2002) 233-254] comprehensi

Existence and Nonexistence of Entire Pos
Existence and Nonexistence of Entire Positive Solutions of Semilinear Elliptic Systems
✍ Xuefeng Wang; Aihua W. Wood πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 80 KB

We show that entire positive solutions exist for the semilinear elliptic system u = p x v Ξ± , v = q x u Ξ² on R N , N β‰₯ 3, for positive Ξ± and Ξ², provided that the nonnegative functions p and q are continuous and satisfy appropriate decay conditions at infinity. We also show that entire solutions fail