Blow-up solutions and global solutions for a class of quasilinear parabolic equations with robin boundary conditions

AbstractThe type of problem under consideration isut=∇⋅(a(u)b(x)∇u)+g(x,t)f(u),inD×(0,T),∂u∂n+σ(x,t)u=0,on∂D×(0,T),u(x,0)=u0(x)>0,inD_where D is a smooth bounded domain of RN. By constructing an auxiliary function and using Hopf's maximum principles on it, existence theorems of blow-up solutions, upper bound of ‘blow-up time”, upper estimates of “blow-up rate”, existence theorems of global solutions and upper estimates of global solutions are given under suitable assumptions on a, b, f, g, σ, and initial data u0(x). The obtained results are applied to some examples in which a, b, f, g, and σ are power functions or exponential functions