Abstract
In the present paper, the blow up of smooth local solutions for a class of nonlinear parabolic equations u, t= ∇(a(u) ∇u)+f(x,u,q,t) (q=| ∇u| 2) with Dirichlet boundary conditions are studied. By constructing an auxiliary function and using Hopf's maximum principles on it, the sufficient conditions for blow-up solutions are obtained and the upper bound of “blow-up time” is given under some suitable assumptions on a, f and initial date. The obtained results are applied to some examples in which a and f are exponential functions.
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