On the Laplace equation with dynamical boundary conditions of reactive-diffusive type

DOI10.1016/j.jmaa.2009.01.023zbMath1167.35019OpenAlexW2038059005MaRDI QIDQ1018325

Enzo Vitillaro, Juan Luis Vazquez

Publication date: 19 May 2009

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2009.01.023

zbMATH Keywords

Laplace equationreactive termsdynamical boundary conditions

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Nonlinear boundary value problems for linear elliptic equations (35J65) Nonlinear elliptic equations (35J60) Transform methods (e.g., integral transforms) applied to PDEs (35A22) Solutions to PDEs in closed form (35C05)

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Cites Work

• Parabolic problems with dynamical boundary conditions: eigenvalue expansions and blow up
• Heat equation with dynamical boundary conditions of locally reactive type
• Semigroups of linear operators and applications to partial differential equations
• Global existence and nonexistence for semilinear parabolic systems with nonlinear boundary conditions
• Nonlinear elliptic systems with dynamic boundary conditions
• On the qualitative behaviour of some semilinear parabolic problems
• The heat equation with generalized Wentzell boundary condition.
• Global nonexistence without blow-up for an evolution problem
• Derivation and physical interpretation of general boundary conditions
• Le spectre d'une variété riemannienne. (The spectrum of a Riemannian manifold)
• Quasilinear parabolic systems with dynamical boundary conditions
• Evolution equations with dynamic boundary conditions
• Heat Equation with Dynamical Boundary Conditions of Reactive Type
• The blow‐up rate for the heat equation with a non‐linear boundary condition
• STABLE EQUILIBRIA TO ELLIPTIC EQUATIONS IN UNBOUNDED DOMAINS WITH NONLINEAR DYNAMIC BOUNDARY CONDITIONS
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