## Differential and Integral Equations

- Differential Integral Equations
- Volume 12, Number 4 (1999), 453-469.

### Existence of global solutions and energy decay for the Carrier equation with dissipative term

Alfredo Tadeu Cousin, Cícero Lopes Frota, and Nickolai A. Lar'kin

#### Abstract

We prove the existence and uniqueness of global solutions to the mixed problem for the Carrier equation $$ u_{tt} - M(\int_{\Omega} u^{2}\, dx ) \Delta u + g(u_{t}) = f, $$ where $g^{\prime}(s) \geq 0, \, 0 < m_{0} \leq M(\lambda)$ and no "smallness" conditions are imposed on the initial data. Moreover, the algebraic and exponential decays of the energy are proved.

#### Article information

**Source**

Differential Integral Equations, Volume 12, Number 4 (1999), 453-469.

**Dates**

First available in Project Euclid: 29 April 2013

**Permanent link to this document**

https://projecteuclid.org/euclid.die/1367267003

**Mathematical Reviews number (MathSciNet)**

MR1697244

**Zentralblatt MATH identifier**

1014.35060

**Subjects**

Primary: 35L70: Nonlinear second-order hyperbolic equations

#### Citation

Frota, Cícero Lopes; Cousin, Alfredo Tadeu; Lar'kin, Nickolai A. Existence of global solutions and energy decay for the Carrier equation with dissipative term. Differential Integral Equations 12 (1999), no. 4, 453--469. https://projecteuclid.org/euclid.die/1367267003