Diffusion phenomenon for linear dissipative wave equations

Handle URI:
http://hdl.handle.net/10754/562006
Title:
Diffusion phenomenon for linear dissipative wave equations
Authors:
Said-Houari, Belkacem
Abstract:
In this paper we prove the diffusion phenomenon for the linear wave equation. To derive the diffusion phenomenon, a new method is used. In fact, for initial data in some weighted spaces, we prove that for {equation presented} decays with the rate {equation presented} [0,1] faster than that of either u or v, where u is the solution of the linear wave equation with initial data {equation presented} [0,1], and v is the solution of the related heat equation with initial data v 0 = u 0 + u 1. This result improves the result in H. Yang and A. Milani [Bull. Sci. Math. 124 (2000), 415-433] in the sense that, under the above restriction on the initial data, the decay rate given in that paper can be improved by t -γ/2. © European Mathematical Society.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Publisher:
European Mathematical Publishing House
Journal:
Zeitschrift für Analysis und ihre Anwendungen
Issue Date:
2012
DOI:
10.4171/ZAA/1459
Type:
Article
ISSN:
02322064
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorSaid-Houari, Belkacemen
dc.date.accessioned2015-08-03T09:36:05Zen
dc.date.available2015-08-03T09:36:05Zen
dc.date.issued2012en
dc.identifier.issn02322064en
dc.identifier.doi10.4171/ZAA/1459en
dc.identifier.urihttp://hdl.handle.net/10754/562006en
dc.description.abstractIn this paper we prove the diffusion phenomenon for the linear wave equation. To derive the diffusion phenomenon, a new method is used. In fact, for initial data in some weighted spaces, we prove that for {equation presented} decays with the rate {equation presented} [0,1] faster than that of either u or v, where u is the solution of the linear wave equation with initial data {equation presented} [0,1], and v is the solution of the related heat equation with initial data v 0 = u 0 + u 1. This result improves the result in H. Yang and A. Milani [Bull. Sci. Math. 124 (2000), 415-433] in the sense that, under the above restriction on the initial data, the decay rate given in that paper can be improved by t -γ/2. © European Mathematical Society.en
dc.publisherEuropean Mathematical Publishing Houseen
dc.subjectAsymptotic behavioren
dc.subjectCauchy problemen
dc.subjectDamped wave equationen
dc.subjectDiffusion phenomenonen
dc.subjectHeat equationen
dc.titleDiffusion phenomenon for linear dissipative wave equationsen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalZeitschrift für Analysis und ihre Anwendungenen
kaust.authorSaid-Houari, Belkacemen
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