Differential and Integral Equations

Energy decay for the wave equation in exterior domains with some half-linear dissipation

Il Hyo Jung and Mitsuhiro Nakao

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We study the decay estimates of the energy for the wave equation in an exterior domain with a localized dissipation. The dissipative term consists of the following two parts: The first part may be nonlinear and localized in a suitable bounded area, while the second part is linear in the outside of a big ball. So we may call such a dissipation ``half-linear" dissipation. We note that no geometrical condition is imposed on the boundary. As an application of the decay estimates we prove some global existence theorems for the wave equation with a nonlinear source term.

Article information

Differential Integral Equations, Volume 16, Number 8 (2003), 927-948.

First available in Project Euclid: 21 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35L70: Nonlinear second-order hyperbolic equations
Secondary: 35B35: Stability 35B40: Asymptotic behavior of solutions


Nakao, Mitsuhiro; Jung, Il Hyo. Energy decay for the wave equation in exterior domains with some half-linear dissipation. Differential Integral Equations 16 (2003), no. 8, 927--948. https://projecteuclid.org/euclid.die/1356060576

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