Well-posedness of the fractional Zener wave equation for heterogeneous viscoelastic materials

DOI10.1515/fca-2020-0005zbMath1439.35544arXiv1909.05337OpenAlexW3102635876MaRDI QIDQ2176138

Ljubica Oparnica, Endre Süli

Publication date: 4 May 2020

Published in: Fractional Calculus \& Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1909.05337

zbMATH Keywords

existenceuniquenessviscoelastic materialsfractional Zener model

Mathematics Subject Classification ID

Linear constitutive equations for materials with memory (74D05) PDEs in connection with mechanics of deformable solids (35Q74) Fractional partial differential equations (35R11) Initial-boundary value problems for second-order hyperbolic systems (35L53)

Related Items

A posteriori error analysis for approximations of time-fractional subdiffusion problems ⋮ Determining kernels in linear viscoelasticity ⋮ Indirect stabilization of a coupled system by memory effects ⋮ Analysis of a Dilute Polymer Model with a Time-Fractional Derivative ⋮ An Error Estimate of a Numerical Approximation to a Hidden-Memory Variable-Order Space-Time Fractional Diffusion Equation ⋮ An existence result for the fractional Kelvin-Voigt's model on time-dependent cracked domains ⋮ Energy dissipation for hereditary and energy conservation for non-local fractional wave equations ⋮ On an inverse problem of nonlinear imaging with fractional damping

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Optimal order finite element approximation for a hyperbolic integro-differential equation
• Waves in fractional Zener type viscoelastic media
• Boundedness of weak solutions to evolutionary partial integro-differential equations with discontinuous coefficients
• A modified Zener model of a viscoelastic body
• Discontinuous Galerkin method for an integro-differential equation modeling dynamic fractional order viscoelasticity
• Greedy approximation of high-dimensional Ornstein-Uhlenbeck operators
• ANALYSIS OF FOUR-PARAMETER FRACTIONAL DERIVATIVE MODEL OF REAL SOLID MATERIALS
• On the Fractional Calculus Model of Viscoelastic Behavior
• Reflections on Dubinskiĭ’s nonlinear compact embedding theorem