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Propagation of perturbations in thin capillary film equations with nonlinear diffusion and convection. (Russian, English) Zbl 1150.35445

Sib. Mat. Zh. 47, No. 4, 914-931 (2006); translation in Sib. Math. J. 47, No. 4, 751-766 (2006).
Summary: We study the evolution of the support of an arbitrary strong generalized solution to the Cauchy problem for the thin film equation with nonlinear diffusion and convection. We find an upper bound exact (in a sense) for the propagation speed of the support of this solution.

MSC:

35K55 Nonlinear parabolic equations
35K65 Degenerate parabolic equations
35Q35 PDEs in connection with fluid mechanics
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