## Differential and Integral Equations

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

#### 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