## Differential and Integral Equations

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

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

Il Hyo Jung and Mitsuhiro Nakao

#### Abstract

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

**Source**

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

**Dates**

First available in Project Euclid: 21 December 2012

**Permanent link to this document**

https://projecteuclid.org/euclid.die/1356060576

**Mathematical Reviews number (MathSciNet)**

MR1988953

**Zentralblatt MATH identifier**

1035.35013

**Subjects**

Primary: 35L70: Nonlinear second-order hyperbolic equations

Secondary: 35B35: Stability 35B40: Asymptotic behavior of solutions

#### Citation

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