On boundedness of solutions of reaction-diffusion equations with nonlinear boundary conditions
José M. Arrieta · Proceedings of the American Mathematical Society · 2007
We give conditions on the nonlinearities of a reaction-diffusion equation with nonlinear boundary conditions that guarantee that any solution starting at bounded initial data is bounded locally around a certain point x 0 x_0 of the boundary, uniformly for all positive time. The conditions imposed are of a local nature and need only to hold in a small neighborhood of the point x 0 x_0 .