Electron. J. Diff. Equ., Vol. 2011 (2011), No. 65, pp. 1-18.

Scattering for wave equations with dissipative terms in layered media

Mitsuteru Kadowaki, Hideo Nakazawa, Kazuo Watanabe

In this article, we show the existence of scattering solutions to wave equations with dissipative terms in layered media. To analyze the wave propagation in layered media, it is necessary to handle singular points called thresholds in the spectrum. Our main tools are Kato's smooth perturbation theory and some approximate operators.

Submitted January 23, 2011. Published May 17, 2011.
Math Subject Classifications: 35P25, 47A40.
Key Words: Layered media; wave equation; dissipative terms; scattering; threshold; Kato's smooth perturbation.

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Mitsuteru Kadowaki
Department of Mechanical Engineering
Ehime University, 3 Bunkyo-cho
Matsuyama, 790-8577, Japan
email: kadowaki.mitsuteru.mz@ehime-u.ac.jp
Hideo Nakazawa
Department of Mathematics
Chiba Institute of Technology
2-1-1 Shibazono
Narashino, Chiba 275-0023, Japan
email: nakazawa.hideo@it-chiba.ac.jp
Kazuo Watanabe
Department of Mathematics, Gakushuin University
1-5-1 Mejiro, Toshima-ku, Tokyo 171-8588, Japan
email: kazuo.watanabe@gakushuin.ac.jp

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