Blow-up solutions for a class of nonlinear parabolic equations with Dirichlet boundary conditions Original Research Article

In the present paper, the blow up of smooth local solutions for a class of nonlinear parabolic equations View the MathML source with Dirichlet boundary conditions are studied. By constructing an auxiliary function and using Hopfʹs 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.