The Lyapunov method for semigroups of nonlinear contractions in Banach spaces

DOI10.1007/BF02790164zbMath0507.47042OpenAlexW2022154071MaRDI QIDQ1837385

A. Pazy

Publication date: 1981

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02790164

zbMATH Keywords

accretive operatorinitial value problemLyapunov functionsLyapunov's methodsemigroups of nonlinear contractions

Mathematics Subject Classification ID

Semigroups of nonlinear operators (47H20) Nonlinear accretive operators, dissipative operators, etc. (47H06) Equations involving nonlinear operators (general) (47J05)

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Cites Work

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• Nonlinear parabolic equations involving measures as initial conditions
• Semi-linear second-order elliptic equations in \(L^1\)
• Semi-groups of nonlinear contractions and dissipative sets
• L^PBounds of solutions of reaction-diffusion equations
• Effets régularisants de semi-groupes non linéaires dans des espaces de Banach
• Shorter Notes: Strongly Continuous Semigroups, Weak Solutions, and the Variation of Constants Formula
• Regularity properties for the heat equation subject to nonlinear boundary constraints
• Generation of Semi-Groups of Nonlinear Transformations on General Banach Spaces
• Lyapunov functions and autonomous differential equations in a Banach space