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 |