Exponential decay bounds for nonlinear heat problems with Robin boundary conditions (Q1001477)

The authors consider a nonlinear parabolic problem which models a heat conduction process on a bounded domain in \(\mathbb R^2\). It is supposed that the linear radiation (Robin) conditions are prescribed on the boundary. The behavior of solutions of the considered problem is investigated. The authors establish certain conditions on the geometry and data sufficient to preclude the blow up of the solution and to obtain an exponential decay bound for the solution and its gradient.