IJPAM: Volume 5, No. 1 (2003)

DECAY ESTIMATES BY MOMENTS AND MASSES
OF INITIAL DATA FOR LINEAR DAMPED
WAVE EQUATIONS

Ryo Ikehata
Department of Mathematics
Graduate School of Education
Hiroshima University
Higashi-Hiroshima 739-8524, JAPAN
e-mail: ikehatar@hiroshima-u.ac.jp


Abstract.We present new decay estimates of solutions to the Cauchy problem of an equation $v_{tt}- v_{xx} + v_{t} = 0$, which has a moment type of weighted initial data
$[v_{0},v_{1}] \in (H^{1}({\bf R})\cap L^{1,2(k+1)}({\bf R})) \times (L^{2}({\bf R})\cap L^{1,2(k+1)}({\bf R}))$
(for definition of $L^{1,\gamma}({\bf R})$, see below) with $k \in {\bf N}$.

Received: February 14, 2003

AMS Subject Classification: 35B40, 35L70

Key Words and Phrases: damped wave equation, Cauchy problem, moment, mass, fast decay

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2003
Volume: 5
Issue: 1