Semigroups of locally Lipschitz operators associated with semilinear evolution equations of parabolic type

DOI10.1016/j.na.2007.10.035zbMath1169.47045OpenAlexW2011529600MaRDI QIDQ2378825

Naoki Tanaka, Toshitaka Matsumoto

Publication date: 14 January 2009

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2007.10.035

zbMATH Keywords

mild solutionsanalytic semigroupssmoothing effectinfinitesimal generatorscomplex Ginzburg-Landau equationfractional powersemilinear evolution equations of parabolic typesemigroups of locally Lipschitz operators

Mathematics Subject Classification ID

Semigroups of nonlinear operators (47H20) Abstract parabolic equations (35K90) Nonlinear differential equations in abstract spaces (34G20) Perturbations of nonlinear operators (47H14)

Related Items (5)

Existence and decay estimates of solutions to complex Ginzburg-Landau type equations ⋮ A simple approach to the Cauchy problem for complex Ginzburg-Landau equations by compactness methods ⋮ Monotonicity method applied to complex Ginzburg-Landau type equations ⋮ A product formula for semigroups of Lipschitz operators associated with semilinear evolution equations of parabolic type ⋮ Operator theory in the complex Ginzburg-Landau equation

Cites Work

• Semigroups of locally Lipschitz operators associated with semilinear evolution equations
• Semigroups of linear operators and applications to partial differential equations
• On semilinear parabolic evolution equations on closed sets
• Geometric theory of semilinear parabolic equations
• A remark on flow invariance for semilinear parabolic equations
• Some results on Liapunov functions and generated dynamical systems
• Invariant sets and existence theorems for semilinear parabolic and elliptic systems
• Semi-groups of local Lipschitzians in a Banach space
• On the generation of unbounded semigroups of bounded linear operators
• Differential Equations on Closed Subsets of a Banach Space
• Relatively continuous nonlinear perturbations of analytic semigroups
• Characterization of Nonlinear Semigroups Associated with Semilinear Evolution Equations
• Analytic semigroups and optimal regularity in parabolic problems
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