| Abstract: |
| We are concerned with the initial-boundary value problem for nonlinear parabolic equations governed by nonlinear boundary conditions of radiation type. There are many phenomena for which it is desirable to impose nonlinear boundary conditions corresponding nonlinear radiation law such as Stefan-Boltzmann`s law. However, there are few studies on parabolic equations with nonlinear boundary conditions although they are very important from physical point of view. In this talk we show the existence of strong solutions by applying abstract theory of nonlinear evolution equations and discuss the large time behavior of solutions. Our approach to prove the existence of blow-up solutions is based on some comparison theorem developed by the author and the co-author. |
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