Finite time blow-up for a thin-film equation with initial data at arbitrary energy level

Abstract In this paper, we consider the initial boundary value problem for a class of thin-film equations in R n with a p -Laplace term and a nonlocal source term | u | q − 2 u − 1 | Ω | ∫ Ω | u | q − 2 u dx . We prove that there exist weak solutions for the problem with arbitrarily initial energy that blow up in finite time. We also obtain the upper bounds for the blow-up time.

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