Blow-up phenomena in parabolic problems with time dependent coefficients under Dirichlet boundary conditions

Blow-up phenomena of solutions to nonlinear parabolic equations have been assiduously investigated during the past decade. We refer the reader to the books of Straughan [20] and of Quittner and Souplet [19] as well as to the survey paper of Bandle and Brunner [2] for an account on this matter. Further contributions to the field are [1], [3]–[18], [22]–[24]. It is well known that the solutions may remain bounded for all time, or may blow up in finite or infinite time. When blow-up occurs at time t , the evaluation of t is of great practical interest. Since t is usually not explicitly computable, we want to derive lower and upper bounds for t . The present paper investigates the blow-up phenomena of the solution u(x, t) of the following nonlinear parabolic problem:

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