## Journal of the Mathematical Society of Japan

- J. Math. Soc. Japan
- Volume 56, Number 2 (2004), 365-373.

### Decay estimates of solutions for dissipative wave equations in ${R}^{N}$ with lower power nonlinearities

Ryo IKEHATA, Yasuaki MIYAOKA, and Takashi NAKATAKE

#### Abstract

Optimal energy decay estimates will be derived for weak solutions to the Cauchy problem in ${R}^{N}(N=1,2,3)$ of dissipative wave equations, which have lower power nonlinearities $|u{|}^{p-1}u$ satisfying $$.

#### Article information

**Source**

J. Math. Soc. Japan, Volume 56, Number 2 (2004), 365-373.

**Dates**

First available in Project Euclid: 3 October 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.jmsj/1191418635

**Digital Object Identifier**

doi:10.2969/jmsj/1191418635

**Mathematical Reviews number (MathSciNet)**

MR2048464

**Zentralblatt MATH identifier**

1056.35120

**Subjects**

Primary: 35L70: Nonlinear second-order hyperbolic equations

Secondary: 35B33: Critical exponents

**Keywords**

semilinear wave equation critical exponent dissipation Cauchy problem optimal decay estimates

#### Citation

IKEHATA, Ryo; MIYAOKA, Yasuaki; NAKATAKE, Takashi. Decay estimates of solutions for dissipative wave equations in $R^{N}$ with lower power nonlinearities. J. Math. Soc. Japan 56 (2004), no. 2, 365--373. doi:10.2969/jmsj/1191418635. https://projecteuclid.org/euclid.jmsj/1191418635