L ∞-Energy Method, Basic Tools and Usage

DOI10.1007/978-3-7643-8482-1_27zbMath1152.35400OpenAlexW2269438497MaRDI QIDQ3525269

Mitsuharu Ôtani

Publication date: 12 September 2008

Published in: Progress in Nonlinear Differential Equations and Their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-7643-8482-1_27

zbMATH Keywords

quasilinear parabolic equations

Mathematics Subject Classification ID

Degenerate parabolic equations (35K65) Quasilinear parabolic equations (35K59)

Related Items (10)

Asymptotic limits of viscous Cahn-Hilliard equation with homogeneous Dirichlet boundary condition ⋮ \(L^\infty\)-energy method for a parabolic system with convection and hysteresis effect ⋮ Theory of Invariant Manifolds for Infinite-Dimensional Nonautonomous Dynamical Systems and Applications ⋮ 𝐿^{∞}-Energy method and its applications to nonlinear partial differential equations ⋮ On some quasilinear parabolic equations with non-monotone multivalued terms ⋮ Infinite-dimensional attractors for parabolic equations with \(p\)-Laplacian in heterogeneous medium ⋮ Existence of time periodic solution to some double-diffusive convection system in the whole space domain ⋮ Long time behavior of a parabolic \(p\)-Laplacian equation coupled to a compartmental ODE system with an induction threshold phenomenon ⋮ Control of a multi-component phase transition model with hysteresis ⋮ On a comparison theorem for parabolic equations with nonlinear boundary conditions

Cites Work

• Nonmonotone perturbations for nonlinear parabolic equations associated with subdifferential operators, Cauchy problems
• Uniqueness of solutions of the initial-value problem for \(u_t- \Delta\varphi (u)=0\)
• Lipschitz continuous solutions of some doubly nonlinear parabolic equations
• \(L^\infty\)-energy method for a parabolic system with convection and hysteresis effect
• A method of energy estimates in \(L^\infty\) and its application to porous medium equations
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