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=∇⋅(g(u)∇u)+f(u)in  Ω×(0,T),∂u∂n+γu=0on  ∂Ω×(0,T),u(x,0)=h(x)≥0in  Ω¯, where ΩΩ is a bounded domain of RN(N≥2) with smooth boundary ∂Ω∂Ω. 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.