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A potential well theory for the wave equation with nonlinear source and boundary damping terms

โœ Scribed by Vitillaro E.

Book ID
127451065
Tongue
English
Weight
2 MB
Category
Library

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๐Ÿ“œ SIMILAR VOLUMES

Global existence and nonexistence for a
Global existence and nonexistence for a nonlinear wave equation with damping and source terms
โœ Yong Zhou ๐Ÿ“‚ Article ๐Ÿ“… 2005 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 209 KB

## Abstract In this paper we consider a nonlinear wave equation with damping and source term on the whole space. For linear damping case, we show that the solution blows up in finite time even for vanishing initial energy. The criteria to guarantee blowup of solutions with positive initial energy a

Existence of a Solution of the Wave Equa
Existence of a Solution of the Wave Equation with Nonlinear Damping and Source Terms
โœ V. Georgiev; G. Todorova ๐Ÿ“‚ Article ๐Ÿ“… 1994 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 375 KB

We study the nonlinear wave equation involving the nonlinear damping term \(u_{i}\left|u_{t}\right|^{m-1}\) and a source term of type \(u|u|^{p-1}\). For \(1<p \leqslant m\) we prove a global existence theorem with large initial data. For \(1<m<p\) a blow-up result is established for sufficiently la