TY - JOUR

T1 - Diffusion phenomenon for linear dissipative wave equations

AU - Said-Houari, Belkacem

N1 - KAUST Repository Item: Exported on 2020-10-01

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10754/562006

UR - http://www.ems-ph.org/doi/10.4171/ZAA/1459

UR - http://www.scopus.com/inward/record.url?scp=84863919164&partnerID=8YFLogxK

U2 - 10.4171/ZAA/1459

DO - 10.4171/ZAA/1459

M3 - Article

SN - 0232-2064

VL - 31

SP - 267

EP - 282

JO - Zeitschrift für Analysis und ihre Anwendungen

JF - Zeitschrift für Analysis und ihre Anwendungen

IS - 3

ER -