LOCAL EXISTENCE AND BLOW UP IN NONLINEAR THERMOELASTICITY WITH SECOND SOUND

DOI10.1081/PDE-120005852zbMath1014.35001MaRDI QIDQ3149944

Messaoudi A. Salim

Publication date: 8 July 2003

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

zbMATH Keywords

energy methodfinite time blow-upBanach contraction mapping principlesemilinear systemlocal strong solutionsmultidimensional thermoelasticity

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Singularities, blow-up, stress concentrations for dynamical problems in solid mechanics (74H35) Thermal effects in solid mechanics (74F05) Long-time behavior of solutions for dynamical problems in solid mechanics (74H40)

Related Items (10)

General Decay Result for a Weakly Damped Thermo-Viscoelastic System with Second Sound ⋮ General boundary stabilization of memory type in thermoelasticity of type III ⋮ Blow up of solutions of systems of nonlinear equations of thermoelasticity ⋮ Boundary stabilization of memory-type thermoelasticity with second sound ⋮ A new result for a blow-up of solutions to a logarithmic flexible structure with second sound ⋮ A general decay result for a multi-dimensional weakly damped thermoelastic system with second sound ⋮ Exponential stability for nonlinear thermoelastic equations with second sound ⋮ Boundary stabilization of memory type in thermoelasticity of type III ⋮ Nonlinear damped Timoshenko systems with second sound-Global existence and exponential stability ⋮ A general decay result for a memory-type thermoelasticity with second sound

Cites Work

• On formation of singularities in one-dimensional nonlinear thermoelasticity
• Global existence, uniqueness, and asymptotic stability of classical smooth solutions in one-dimensional nonlinear thermoelasticity
• Global smooth solutions and asymptotic stability in one-dimensional nonlinear thermoelasticity
• Well-posed quasi-linear second-order hyperbolic systems with applications to nonlinear elastodynamics and general relativity
• Propagation of singularities in one-dimensional thermoelasticity
• Nonlinear boundary stabilization of an inhomogeneous and anisotropic thermoelasticity system
• Blow-up in non-linear three-dimensional thermoelasticity
• Development of singularities in solutions of the equations of nonlinear thermoelasticity
• On the existence of smooth solutions in one-dimensional nonlinear thermoelasticity with second sound
• Existence and exponential decay in nonlinear thermoelasticity
• Smoothing Properties, Decay, and Global Existence of Solutions to Nonlinear Coupled Systems of Thermoelastic Type
• A nonexistence result to a Cauchy problem in nonlinear one-dimensional thermoelasticity

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