Mild and strong solutions for partial differential equations with delay

DOI10.1007/BF01789412zbMath0518.35077OpenAlexW2073202741MaRDI QIDQ1053893

Wilhelm Schappacher, Karl Kunisch

Publication date: 1980

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01789412

zbMATH Keywords

reflexive Banach spacenonlinear functional differential equationnonlinear (local) semigroup theorynotions of solutions

Mathematics Subject Classification ID

Semigroups of nonlinear operators (47H20) Smoothness and regularity of solutions to PDEs (35B65) Partial functional-differential equations (35R10)

Related Items

Linearized Stability for Nonlinear Partial Differential Delay Equations, Flow invariance for nonlinear partial differential delay equations, Necessary conditions for partial differential equations with delay to generate \(C_ 0\)-semigroups

Cites Work

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• On the initial value problem for a class of functional-differential equations
• Nonlinear evolution equations in an arbitrary Banach space
• Nonlinear semigroups of translations in Banach space generated by functional differential equations
• Semilinear functional differential equations in Banach space
• Nonlinear semigroups and evolution equations
• Existence, Stability, and Compactness in the α-Norm for Partial Functional Differential Equations
• Non-linear functional differential equations and abstract integral equations
• Variation of constants formulas for partial differential equations with delay
• Existence and Stability for Partial Functional Differential Equations
• 20.—Functional Differential Equations and Non-linear Evolution Operators
• Nonlinear functional differential equations in L1 spaces
• Hereditary Control Problems: Numerical Methods Based on Averaging Approximations
• Autonomous nonlinear functional differential equations and averaging approximations
• On the radial projection in normed spaces
• Generation of Semi-Groups of Nonlinear Transformations on General Banach Spaces
• Nonlinear evolution equations in Banach spaces