Differential and Integral Equations

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

Song Jiang and Jaime E. Muñoz Rivera

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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

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

First available in Project Euclid: 7 May 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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

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