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Global nonexistence of solutions to a semilinear wave equation in the Minkowski space

โœ Scribed by Xuefei Liu; Yong Zhou

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
209 KB
Volume
21
Category
Article
ISSN
0893-9659

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โœฆ Synopsis

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] comprehensively. Due to a modification of the so-called method of conformal compactification used by Belchev, Kepka and Zhou, we show that the solutions blow up in finite time with more relaxed initial data and extended index p.

๐Ÿ“œ SIMILAR VOLUMES

Existence and nonexistence of global sol
Existence and nonexistence of global solutions of some system of semilinear wave equations
โœ Meng-Rong Li; Long-Yi Tsai ๐Ÿ“‚ Article ๐Ÿ“… 2003 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 213 KB

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.

Parametric Resonance and Nonexistence of
Parametric Resonance and Nonexistence of the Global Solution to Nonlinear Wave Equations
โœ Karen Yagdjian ๐Ÿ“‚ Article ๐Ÿ“… 2001 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 144 KB

We give an example of the influence of the dependence of the coefficient of equation on time variable, and in particular oscillations in time, on a global existence of the solution to the nonlinear hyperbolic equation. Namely for arbitrary small initial data we construct a blowing up solution.