An analytic semigroup setting for a class of Volterra equations

DOI10.1216/jiea/1181074916zbMath1041.45010OpenAlexW2028581241MaRDI QIDQ1425611

Philippe Clément, Wolfgang Desch, K. W. Homan

Publication date: 17 March 2004

Published in: Journal of Integral Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1216/jiea/1181074916

zbMATH Keywords

regularity of solutionsinterpolation methodscompletely monotonic kernelsemigroup settingVolterra integrodifferential equation of convolution type

Mathematics Subject Classification ID

Integro-ordinary differential equations (45J05) Groups and semigroups of linear operators (47D03) Integro-differential operators (47G20)

Related Items (6)

Volterra equations in Banach spaces with completely monotone kernels ⋮ Some approximation results for mild solutions of stochastic fractional order evolution equations driven by Gaussian noise ⋮ An analytic approach to stochastic Volterra equations with completely monotone kernels ⋮ An analytic semigroup setting for a class of Volterra equations ⋮ Controllability of a class of Volterra equations in Hilbert spaces with completely monotone kernel ⋮ Stress obtained by interpolation methods for a boundary value problem in linear viscoelasticity

Cites Work

• Semigroups of linear operators and applications to partial differential equations
• One-parameter semigroups of positive operators
• Exponential stabilization of Volterra integral equations with singular kernels
• An analytic semigroup setting for a class of Volterra equations
• Singular Relaxation Moduli and Smoothing in Three-Dimensional Viscoelasticity
• Evolutionary Integral Equations and Applications
• Well-Posedness and Stabilizability of a Viscoelastic Equation in Energy Space
• Topics in Harmonic Analysis Related to the Littlewood-Paley Theory. (AM-63)
• Analytic semigroups and optimal regularity in parabolic problems
• Stochastic Equations in Infinite Dimensions
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