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

F. Gazzola; Marco Squassina

doi:10.1016/j.anihpc.2005.02.007

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

F. Gazzola^*, Marco Squassina

^*Autore corrispondente per questo lavoro

Risultato della ricerca: Contributo in rivista › Articolo › 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\r\nwhich the solution blows up are constructed.

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

All Science Journal Classification (ASJC) codes

Analisi
Fisica Matematica
Matematica Applicata

Keywords

damped semilinear wave

Accesso al documento

10.1016/j.anihpc.2005.02.007

Altri file e collegamenti

Cita questo

@article{1f4fc4e015994366acf9d685cd7a99c6,

title = "Global solutions and finite time blow up for damped semilinear wave equations",

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\textbackslash{}r\textbackslash{}nwhich the solution blows up are constructed.",

keywords = "damped semilinear wave, damped semilinear wave",

author = "F. Gazzola and Marco Squassina",

year = "2006",

doi = "10.1016/j.anihpc.2005.02.007",

language = "English",

volume = "23",

pages = "185--207",

journal = "ANNALES DE L INSTITUT HENRI POINCAR{\'E}. ANALYSE NON LIN{\'E}AIRE",

issn = "0294-1449",

publisher = "Attuale: Paris: Elsevier 1998- Gauthier-Villars:15 rue Gossin, 92543 Montrouge Cedex France:011 33 1 40 926500, Fax: 011 33 1 40 926597",

number = "N/A",

}

TY - JOUR

T1 - Global solutions and finite time blow up for damped semilinear wave equations

AU - Gazzola, F.

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\r\nwhich 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\r\nwhich the solution blows up are constructed.

KW - damped semilinear wave

UR - https://publicatt.unicatt.it/handle/10807/91012

UR - https://www.scopus.com/inward/citedby.uri?partnerID=HzOxMe3b&scp=31344442872&origin=inward

UR - https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=31344442872&origin=inward

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

IS - N/A

ER -

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

Abstract

All Science Journal Classification (ASJC) codes

Keywords

Accesso al documento

Altri file e collegamenti

Fingerprint

Cita questo