Regularity and asymptotic behavior for the second order parabolic equation with nonlinear boundary conditions

DOI10.1016/0022-0396(81)90063-2zbMath0501.35045OpenAlexW1964506284MaRDI QIDQ1172207

Nicholas D. Alikakos

Publication date: 1981

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-0396(81)90063-2

zbMATH Keywords

uniquenessglobal existencenonlinear boundary conditionsattracting stable equilibriacompactness of the orbits

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations (35K60) Initial-boundary value problems for second-order parabolic equations (35K20) Groups and semigroups of linear operators (47D03)

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Cites Work

• Étude de la solution fondamentale de l'équation parabolique
• Propriétés des dérivées tangentielles d'une intégrale de l'équation parabolique
• Semigroups of linear operators and applications to partial differential equations
• Stabilization of concentration profiles in catalyst particles
• Global stability of symmetric and asymmetric concentration profiles in catalyst particles
• The Hopf bifurcation and its applications. With contributions by P. Chernoff, G. Childs, S. Chow, J. R. Dorroh, J. Guckenheimer, L. Howard, N. Kopell, O. Lanford, J. Mallet-Paret, G. Oster, O. Ruiz, S. Schecter, D. Schmidt, and S. Smale
• Asymptotic behavior and nonexistence of global solutions for a class of nonlinear boundary value problems of parabolic type
• Dynamical systems and stability
• Singular integrals
• A bifurcation problem for a nonlinear partial differential equation of parabolic type^†
• Regularity properties for the heat equation subject to nonlinear boundary constraints
• An Infinite Dimensional Version of Sard's Theorem
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