Global solutions and finite time blow up for damped semilinear wave equations

Filippo Gazzola; Marco Squassina

doi:10.1016/j.anihpc.2005.02.007

Global solutions and finite time blow up for damped semilinear wave equations

Filippo Gazzola, Marco Squassina

Polytechnic University of Milan

Risultato della ricerca: Contributo in rivista › Articolo in rivista › peer review

144 Citazioni (Scopus)

Abstract

A class of damped wave equations with superlinear source term is considered. It is shown that every global solution is uniformly bounded in the natural phase space. Global existence of solutions with initial data in the potential well is obtained. Finally, not only finite time blow up for solutions starting in the unstable set is proved, but also high energy initial data for which the solution blows up are constructed.

Lingua originale	English
pagine (da-a)	185-207
Numero di pagine	23
Rivista	ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE
Volume	23
DOI	https://doi.org/10.1016/j.anihpc.2005.02.007
Stato di pubblicazione	Pubblicato - 2006

Keywords

damped semilinear wave

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10.1016/j.anihpc.2005.02.007

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abstract = "A class of damped wave equations with superlinear source term is considered. It is shown that every global solution is uniformly bounded in the natural phase space. Global existence of solutions with initial data in the potential well is obtained. Finally, not only finite time blow up for solutions starting in the unstable set is proved, but also high energy initial data for which the solution blows up are constructed.",

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AU - Gazzola, Filippo

AU - Squassina, Marco

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AB - A class of damped wave equations with superlinear source term is considered. It is shown that every global solution is uniformly bounded in the natural phase space. Global existence of solutions with initial data in the potential well is obtained. Finally, not only finite time blow up for solutions starting in the unstable set is proved, but also high energy initial data for which the solution blows up are constructed.

KW - damped semilinear wave

UR - http://hdl.handle.net/10807/91012

U2 - 10.1016/j.anihpc.2005.02.007

DO - 10.1016/j.anihpc.2005.02.007

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JO - ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE

JF - ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE

ER -

Global solutions and finite time blow up for damped semilinear wave equations

Abstract

Keywords

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