Semigroups and nonlinear evolution equations

DOI10.1016/0024-3795(86)90305-8zbMath0624.35047OpenAlexW1979876294MaRDI QIDQ1092235

Herbert Amann

Publication date: 1986

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0024-3795(86)90305-8

zbMATH Keywords

surveyexistenceuniquenessnonlinear boundary conditionsquasilinearinfinitesimal generatorsemiflowvariation of constants formulasemilinearreaction diffusionstrongly parabolicstrongly continuous analytic semigroupunique maximal solution

Mathematics Subject Classification ID

Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations (35K60) Reaction-diffusion equations (35K57) Integral representations of solutions to PDEs (35C15) Groups and semigroups of linear operators (47D03) Dilations, extensions, compressions of linear operators (47A20)

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Cites Work

• Formule de Duhamel abstraite. (Abstract Duhamel formula)
• Semigroups of linear operators and applications to partial differential equations
• Parabolic equations with nonlinear time-dependent boundary conditions
• Maximal regularity for evolution equations by interpolation and extrapolation
• Quasilinear parabolic systems under nonlinear boundary conditions
• Boundary feedback stabilizability of parabolic equations
• Unified theory for abstract parabolic boundary problems - a semigroup approach
• Geometric theory of semilinear parabolic equations
• Regularity and asymptotic behavior for the second order parabolic equation with nonlinear boundary conditions
• On abstract parabolic fundamental solutions
• Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105)
• Reaction diffusion equations with nonlinear boundary conditions
• Global existence for semilinear parabolic systems.
• Quasilinear Evolution Equations and Parabolic Systems
• Semi-linear evolution equations in interpolation spaces
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