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

Research output: Contribution to journal › Article › peer-review

144 Citations (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.

Original language	English
Pages (from-to)	185-207
Number of pages	23
Journal	ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE
Volume	23
DOIs	https://doi.org/10.1016/j.anihpc.2005.02.007
Publication status	Published - 2006

Keywords

damped semilinear wave

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10.1016/j.anihpc.2005.02.007

Cite this

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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

PY - 2006

Y1 - 2006

N2 - 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.

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

M3 - Article

SN - 0294-1449

VL - 23

SP - 185

EP - 207

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

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Keywords

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