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The thin film equation with \(2\leq n < 3\): Finite speed of propagation in terms of the \(L^1\)-norm. (English) Zbl 0953.35072
Authors’ abstract: We consider the equation \(u_t+(u^n u_{xxx})_x=0\) with \(2\leq n<3\) and establish an estimate for the finite speed of propagation of the support of compactly supported nonnegative solutions. The estimate depends only on the \(L^1\)-norm and is valid a posteriori for strong solutions obtained through a Bernis-Friedman regularization.

MSC:
35K65 Degenerate parabolic equations
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35K55 Nonlinear parabolic equations
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