A qualitative theory for parabolic problems under dynamical boundary conditions

被引：24

作者：

von Below, J ^{[1
]}

De Coster, C ^{[1
]}

机构：

[1] Univ Littoral Cote Dopale, LMPA Joseph Liouville, EA 2597, F-62228 Calais, France

来源：

JOURNAL OF INEQUALITIES AND APPLICATIONS | 2000年 / 5卷 / 05期

关键词：

parabolic problems; dynamical boundary conditions; maximum and comparison principles; upper and lower solutions; convergence to equilibria;

D O I：

10.1155/S1025583400000266

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For nonlinear parabolic problems in a bounded domain under dynamical boundary conditions, general comparison techniques are established similar to the ones under Neumann or Dirichlet boundary conditions. In particular, maximum principles and basic a priori estimates are derived, as well as lower and upper solution techniques that lead to functional band type estimates for classical solutions. Finally, attractivity properties of equilibria are discussed that also illustrate the damping effect of the dissipative dynamical boundary condition.

引用

页码：467 / 486

页数：20

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