A potential well theory for the heat equation with a nonlinear boundary condition
Abstract
Potential well arguments have been used elsewhere to provide precise conditions on initial data which determine existence or nonexistence of global solutions of nonlinear parabolic and hyperbolic initial boundary value problems. In a previous paper, the authors showed that an analogous potential well theory and sharp existencenonexistence alternative can be developed for a linear wave equation problem with a nonlinear boundary constraint. Here, the argument of the previous work is applied to obtain a sharp existencenonexistence alternative for solutions to the linear heat equation subject to a nonlinear boundary condition.
 Publication:

Mathematical Methods in the Applied Sciences
 Pub Date:
 1987
 DOI:
 10.1002/mma.1670090111
 Bibcode:
 1987MMAS....9..127L
 Keywords:

 Boundary Conditions;
 Boundary Value Problems;
 Heat Transfer Coefficients;
 Nonlinear Equations;
 Potential Theory;
 Wells;
 Computational Fluid Dynamics;
 Equations Of Motion;
 Existence Theorems;
 Fluid Mechanics and Heat Transfer