On the motion of a viscoelastic solid in presence of a rigid wall. I. Darboux and general Cauchy problems for a third-order hyperbolic operator: Explicit Riemann function and maximum principles

DOI10.1007/BF00944706zbMath0534.73032MaRDI QIDQ790652

Pasquale Renno, Armando D'Anna, Berardino D'Acunto

Publication date: 1983

Published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik (Search for Journal in Brave)

zbMATH Keywords

perturbationasymptoticminimum principlecompatibilityrigid wallabsence of external forcesDarboux and Cauchy problemsequation for unidimensional motion of a standard linear solidextending the Riemann representation methodinversion formulae of Laplace transformsRiemann function characterized by fundamental solutionthird-order hyperbolic operatorviscoelastic standard linear solid operator

Mathematics Subject Classification ID

General theory of partial differential operators (47F05) Unilateral problems for linear hyperbolic equations and variational inequalities with linear hyperbolic operators (35L85) Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials) (74D99)

Related Items (6)

The MGT-Fourier model in the supercritical case ⋮ Energetic questions about the impact of a viscoelastic solid against an obstacle ⋮ On the Moore-Gibson-Thompson equation with memory with nonconvex kernels ⋮ On the Moore-Gibson-Thompson equation with thermal effects of Gurtin-Pipkin type ⋮ Spectral analysis and stability of the Moore-Gibson-Thompson-Fourier model ⋮ On the Moore-Gibson-Thompson equation and its relation to linear viscoelasticity

Cites Work

• Discontinuous solutions of a nonlinear hyperbolic equation with unilateral constraints
• Continuous solutions of the problem of a string vibrating against an obstacle
• Mouvements périodiques d'une corde vibrante en presence d'un obstacle rectiligne
• On the theory of dissipative three-dimensional wave motion
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