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 language | English (US) |
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Pages (from-to) | 267-282 |
Number of pages | 16 |
Journal | Zeitschrift für Analysis und ihre Anwendungen |
Volume | 31 |
Issue number | 3 |
DOIs | |
State | Published - 2012 |
Bibliographical note
KAUST Repository Item: Exported on 2020-10-01ASJC Scopus subject areas
- Analysis
- Applied Mathematics