Advanced Studies in Pure Mathematics

On the solutions for nonlinear wave equations with localized dissipations in exterior domains

Makoto Nakamura

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Abstract

The Cauchy problem for nonlinear wave equations with localized dissipation is considered in exterior domains outside of compact obstacles in three spatial dimensions. Under the null conditions for the quadratic nonlinear terms, the global solutions are shown for sufficiently small data. The solutions which have different propagation speeds are considered.

Article information

Source
Nonlinear Dynamics in Partial Differential Equations, S. Ei, S. Kawashima, M. Kimura and T. Mizumachi, eds. (Tokyo: Mathematical Society of Japan, 2015), 289-294

Dates
Received: 31 January 2012
First available in Project Euclid: 30 October 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1540934225

Digital Object Identifier
doi:10.2969/aspm/06410289

Mathematical Reviews number (MathSciNet)
MR3381214

Zentralblatt MATH identifier
1342.35165

Subjects
Primary: 35L70: Nonlinear second-order hyperbolic equations

Keywords
Nonlinear wave equations global solutions exterior domains localized dissipations

Citation

Nakamura, Makoto. On the solutions for nonlinear wave equations with localized dissipations in exterior domains. Nonlinear Dynamics in Partial Differential Equations, 289--294, Mathematical Society of Japan, Tokyo, Japan, 2015. doi:10.2969/aspm/06410289. https://projecteuclid.org/euclid.aspm/1540934225


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