Diffusion phenomenon for linear dissipative wave equations

Belkacem Said-Houari

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

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.
Original languageEnglish (US)
Pages (from-to)267-282
Number of pages16
JournalZeitschrift für Analysis und ihre Anwendungen
Volume31
Issue number3
DOIs
StatePublished - 2012

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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