## Differential and Integral Equations

### A global existence theorem for the Dirichlet problem in nonlinear $n$-dimensional viscoelasticity

#### Abstract

We prove the existence and uniqueness of global smooth solutions to the Dirichlet initial-boundary problem in nonlinear $n$-dimensional viscoelasticity of integral type for small initial data in $H^{s_0}(\Omega)$, where $s_0$ is an integer smaller than that needed to establish the local existence. Moreover, the exponential decay of the solution is obtained.

#### Article information

Source
Differential Integral Equations, Volume 9, Number 4 (1996), 791-810.

Dates
First available in Project Euclid: 7 May 2013

https://projecteuclid.org/euclid.die/1367969888

Mathematical Reviews number (MathSciNet)
MR1401438

Zentralblatt MATH identifier
0862.35071

Subjects
Primary: 35L70: Nonlinear second-order hyperbolic equations
Secondary: 35Q72 73F15

#### Citation

Jiang, Song; Muñoz Rivera, Jaime E. A global existence theorem for the Dirichlet problem in nonlinear $n$-dimensional viscoelasticity. Differential Integral Equations 9 (1996), no. 4, 791--810. https://projecteuclid.org/euclid.die/1367969888