Hokkaido Mathematical Journal

Local energy decay for some hyperbolic equations with initial data decaying slowly near infinity

Abstract

A uniform local energy decay property is discussed to a linear hyperbolic equation with spatial variable coefficients. We shall deal with this equation in an exterior domain with a star-shaped complement. Our advantage is that we assume algebraic order weight restrictions as $\vert x\vert \to +\infty$ on the initial data in order to derive the uniform local energy decay, and its proof is quite simple.

Article information

Source
Hokkaido Math. J., Volume 36, Number 1 (2007), 53-71.

Dates
First available in Project Euclid: 29 September 2010

https://projecteuclid.org/euclid.hokmj/1285766662

Digital Object Identifier
doi:10.14492/hokmj/1285766662

Mathematical Reviews number (MathSciNet)
MR2309821

Zentralblatt MATH identifier
1135.35018

Subjects
Primary: 35L05: Wave equation
Secondary: 35B40: Asymptotic behavior of solutions

Citation

IKEHATA, Ryo; SOBUKAWA, Genta. Local energy decay for some hyperbolic equations with initial data decaying slowly near infinity. Hokkaido Math. J. 36 (2007), no. 1, 53--71. doi:10.14492/hokmj/1285766662. https://projecteuclid.org/euclid.hokmj/1285766662