Smoothing for nonlinear parabolic equations with nonlinear boundary conditions (Q1378705)

The authors are concerned with smoothing effects for a class of nonlinear partial differential equations of parabolic type. They extend some known properties of the solution in the linear case, to their nonlinear case. Such properties are: \(u_t(\cdot, t)\to 0\) as \(t\to \infty\) in the \(L^2\)-norm, and \(u(\cdot,t)\) is bounded on \((0,\infty)\) even if the initial condition \(u(0,x) =f(x)\) is merely integrable.