Global solutions to quasi-linear hyperbolic systems of viscoelasticity

DOI10.1215/21562261-1214411zbMath1228.35136OpenAlexW4245429294MaRDI QIDQ542656

Tohru Nakamura, Shuichi Kawashima, Priyanjana M. N. Dharmawardane

Publication date: 10 June 2011

Published in: Kyoto Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/21562261-1214411

zbMATH Keywords

energy methoddampingmemory

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear constitutive equations for materials with memory (74D10) Integro-partial differential equations (35R09) Second-order quasilinear hyperbolic equations (35L72) Initial value problems for second-order hyperbolic systems (35L52)

Related Items (7)

Global existence and decay of small solutions for quasi-linear second-order uniformly dissipative hyperbolic-hyperbolic systems ⋮ Uniform general stability of a coupled Volterra integro-differential equations with fading memories ⋮ Decay property for symmetric hyperbolic system with memory-type diffusion ⋮ Global solutions to the equation of thermoelasticity with fading memory ⋮ Time-weighted energy method for quasi-linear hyperbolic systems of viscoelasticity ⋮ GLOBAL SOLUTIONS AND DECAY PROPERTY WITH REGULARITY-LOSS FOR QUASI-LINEAR HYPERBOLIC SYSTEMS WITH DISSIPATION ⋮ Asymptotic stability in a second-order symmetric hyperbolic system modeling the relativistic dynamics of viscous heat-conductive fluids with diffusion

Cites Work

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• Well-posed quasi-linear second-order hyperbolic systems with applications to nonlinear elastodynamics and general relativity
• Asymptotic behavior of the energy for a class of weakly dissipative second-order systems with memory
• DECAY PROPERTY OF REGULARITY-LOSS TYPE AND APPLICATION TO SOME NONLINEAR HYPERBOLIC–ELLIPTIC SYSTEM
• DECAY PROPERTY OF REGULARITY-LOSS TYPE FOR DISSIPATIVE TIMOSHENKO SYSTEM
• On the exponential stability of linear viscoelasticity and thermoviscoelasticity

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