Regular solutions for time dependent abstract integrodifferential equations with singular kernel

DOI10.1016/0022-247X(88)90382-4zbMath0638.45007MaRDI QIDQ1099368

B. George

Publication date: 1988

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

zbMATH Keywords

regularityexistenceuniquenessanalytic semigrouplinear parabolic Volterra equationtime dependent abstract integrodifferential equations with singular kernel

Mathematics Subject Classification ID

Integro-ordinary differential equations (45J05) Abstract integral equations, integral equations in abstract spaces (45N05)

Related Items

The operator approach to Il'yushin's models of viscoelastic media under the isothermal processes of deformation ⋮ Existence of asymptotically almost periodic solutions for some second-order hyperbolic integrodifferential equations ⋮ Unnamed Item ⋮ Regularity theory for a nonlinear fractional reaction-diffusion equation ⋮ Existence and stability estimate for the solution of the ageing hereditary linear viscoelasticity problem ⋮ Well-posedness and stability results for some nonautonomous abstract linear hyperbolic equations with memory ⋮ Volterra integrodifferential equations of parabolic type of higher order in time in \(L^P\) spaces

Cites Work

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• On the abstract Cauchy problem of parabolic type in spaces of continuous functions
• \(C^{\alpha}\)-regularity for non-autonomous linear integrodifferential equations of parabolic type
• Existence and sharp regularity results for linear parabolic non- autonomous integro-differential equations
• Hölder regularity for non-autonomous abstract parabolic equations
• Interpolation Spaces Between Domains of Elliptic Operators and Spaces of Continuous Functions with Applications to Nonlinear Parabolic Equations
• Generation of Analytic Semigroups by Strongly Elliptic Operators