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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