Blow-up of Solutions for a Class of Nonlinear Parabolic Equations

Abstract

In this paper, the blow up of solutions for a class of nonlinear parabolic equations

with mixed boundary conditions is studied. By constructing an auxiliary function and using Hopf's maximum principles, an existence theorem of blow-up solutions, upper bound of ``blow-up time" and upper estimates of ``blow-up rate" are given under suitable assumptions on $a,b,c,f,g$, initial data and suitable mixed boundary conditions. The obtained result is illustrated through an example in which $a,b,c,f,g$ are power functions or exponential functions.