Advanced Studies in Pure Mathematics
- Adv. Stud. Pure Math.
- Nonlinear Dynamics in Partial Differential Equations, S. Ei, S. Kawashima, M. Kimura and T. Mizumachi, eds. (Tokyo: Mathematical Society of Japan, 2015), 289 - 294
On the solutions for nonlinear wave equations with localized dissipations in exterior domains
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.
Received: 31 January 2012
First available in Project Euclid: 30 October 2018
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Primary: 35L70: Nonlinear second-order hyperbolic equations
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