Global existence and uniform stability of solutions for a quasilinear viscoelastic problem

By Salim A. Messaoudi, Nasser-Eddine Tatar. 2007

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In this paper the nonlinear viscoelastic wave equation in canonical form with Dirichlet boundary condition is considered. By introducing a new functional and using the potential well method, we show that the damping induced by the viscoelastic term is enough to ensure global existence and uniform decay of solutions provided that the initial data are in some stable set. Copyright © 2006 John Wiley & Sons, Ltd.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/46309acfbc9415839c4419bacaf31b91b103db55

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In Computational Theory and Mathematics

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Citations in the corpus

ASYMPTOTIC BEHAVIOR FOR A VISCOELASTIC WAVE EQUATION WITH A DELAY TERM (2013, background): “Recently, Messaoudi and Tatar [15] studied problem (1.”
Existence and a general decay results for a viscoelastic plate equation with a logarithmic nonlinearity (2019, result): “E Tatar, Global existence asymptotic behavior for a non-linear viscoelas- tic problem, Math.”
General decay of solutions of a nonlinear system of viscoelastic wave equations (2011, background): “See in this regard [2,4,7,14,16,17,20,21] and the references therein.”