Continuous dependence results for a class of nonlinear heat equations in a cylindrical region

摘要

In this paper, we derive bounds for the solutions of a quasilinear heat equation in a finite cylindrical region if the far end and the lateral surface are held at zero temperature, and a nonzero temperature is applied at the near end. Some continuous dependence inequalities are also obtained. We also investigate the case in which a given heat flux is prescribed at the near end, instead of a given temperature. Copyright (C) 2008 John Wiley & Sons, Ltd.