Asymptotic behavior of solutions to a quasilinear hyperbolic with nonlinear damping.
Aassila, Mohammed (1998)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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Aassila, Mohammed (1998)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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Haraux, A., Yan, Q. (2001)
Portugaliae Mathematica. Nova Série
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Ye, Yaojun (2010)
Journal of Inequalities and Applications [electronic only]
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Ye, Yaojun (2010)
Advances in Difference Equations [electronic only]
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Cantarelli, Giancarlo (1999)
International Journal of Mathematics and Mathematical Sciences
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Santos, M.L., Ferreira, J., Raposo, C.A. (2005)
Abstract and Applied Analysis
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Park, Jong Yeoul, Bae, Jeong Ja (2000)
International Journal of Mathematics and Mathematical Sciences
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Patrick Martinez (1999)
ESAIM: Control, Optimisation and Calculus of Variations
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Tomáš Bárta (2014)
Commentationes Mathematicae Universitatis Carolinae
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In this paper we consider a model of a one-dimensional body where strain depends on the history of stress. We show local existence for large data and global existence for small data of classical solutions and convergence of the displacement, strain and stress to zero for time going to infinity.
Monica Conti, Stefania Gatti, Vittorino Pata (2007)
Open Mathematics
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This note is concerned with the linear Volterra equation of hyperbolic type on the whole space ℝN. New results concerning the decay of the associated energy as time goes to infinity were established.