## Differential and Integral Equations

- Differential Integral Equations
- Volume 16, Number 6 (2003), 727-736.

### A remark on a critical exponent for the semilinear dissipative wave equation in the one dimensional half space

#### Abstract

We consider the small data global existence of solutions to the $1$-D exterior mixed problem of the equation $u_{tt}-u_{xx} + u_{t} = \vert u\vert^{p}$ . A new lower bound $p = 8/3$ on the nonlinear term and the better decay estimates of solutions can be derived through the new method in [6].

#### Article information

**Source**

Differential Integral Equations, Volume 16, Number 6 (2003), 727-736.

**Dates**

First available in Project Euclid: 21 December 2012

**Permanent link to this document**

https://projecteuclid.org/euclid.die/1356060609

**Mathematical Reviews number (MathSciNet)**

MR1973277

**Zentralblatt MATH identifier**

1036.35143

**Subjects**

Primary: 35L70: Nonlinear second-order hyperbolic equations

Secondary: 35B33: Critical exponents 35L15: Initial value problems for second-order hyperbolic equations

#### Citation

Ikehata, Ryo. A remark on a critical exponent for the semilinear dissipative wave equation in the one dimensional half space. Differential Integral Equations 16 (2003), no. 6, 727--736. https://projecteuclid.org/euclid.die/1356060609