Singular Relaxation Moduli and Smoothing in Three-Dimensional Viscoelasticity

DOI10.2307/2001447zbMath0672.73039OpenAlexW4245446197MaRDI QIDQ3826177

Ronald Grimmer, Wolfgang Desch

Publication date: 1989

Full work available at URL: https://doi.org/10.2307/2001447

zbMATH Keywords

differentiabilityHilbert spacesthermoviscoelasticityequationsrelaxation kernelanalyticity of solutionssemigroup settingsmoothing properties of systems of linear integral and differentialtensor-valued relaxation modulus

Mathematics Subject Classification ID

Integro-partial differential equations (45K05) Bulk waves in solid mechanics (74J10) Linear differential equations in abstract spaces (34G10) Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials) (74D99)

Related Items (14)

Regularity properties of solutions of linear integrodifferential equations with singular kernels ⋮ On a fractional reaction-diffusion equation ⋮ Optimal control for stochastic Volterra equations with multiplicative Lévy noise ⋮ A non-autonomous damped wave equation with a nonlinear memory term ⋮ An analytic semigroup setting for a class of Volterra equations ⋮ Wave propagation in linear viscoelastic media with completely monotonic relaxation moduli ⋮ Controllability of a class of Volterra equations in Hilbert spaces with completely monotone kernel ⋮ Two-fluid porous flow in a single temperature approximation ⋮ Well-Posedness and Stabilizability of a Viscoelastic Equation in Energy Space ⋮ Singular kernel problems in materials with memory ⋮ Energy decay estimates of solutions for viscoelastic damped wave equations in \(\mathbb{R}^N\) ⋮ Passive boundary damping of viscoelastic structures ⋮ Stress obtained by interpolation methods for a boundary value problem in linear viscoelasticity ⋮ Wave propagation in media with singular memory

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