Global and blow-up solutions for nonlinear parabolic equations with Robin boundary conditions

In this paper we discuss the blow-up for classical solutions to the following class of parabolic equations with Robin boundary condition: {(b(u))(t) = del . (g(u)del u) + f(u) in ohm x (0, T), partial derivative u/partial derivative n + gamma u = 0 on partial derivative ohm x (0, T), u(x, 0) = h(x) >= 0 in (ohm) over bar, where ohm is a bounded domain of R-N (N >= 2) with smooth boundary partial derivative ohm. By constructing some appropriate auxiliary functions and using a first-order differential inequality technique, we derive conditions on the data which guarantee the blow-up or the global existence of the solution. For the blow-up solution, a lower bound on blow-up time is also obtained. Moreover, some examples are presented to illustrate the applications. (c) 2013 Elsevier Ltd. All rights reserved.