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Some properties of solutions for the generalized thin film equation in one space dimension. (English) Zbl 1099.35115

Summary: The author studies a generalized thin film equation of the type \[ \frac{\partial u}{\partial t}+\text{div} (|\nabla\Delta u|^{p-2} \nabla\Delta u)=0, \quad x\in\Omega,\;t>0,\;p>2 \] in one space dimension. Some results on the finite speed of propagation of perturbations and regularity of solutions are established.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35K55 Nonlinear parabolic equations
76A20 Thin fluid films
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35B65 Smoothness and regularity of solutions to PDEs
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