Propagation of perturbations for a sixth-order thin film equation

Abstract

We consider an initial-boundary problem for a sixth-order thin film equation, which arises in the industrial application of the isolation oxidation of silicon. Relying on some necessary uniform estimates of the approximate solutions, we prove the existence of radial symmetric solutions to this problem in the two-dimensional space. The nonnegativity and the finite speed of propagation of perturbations of solutions are also discussed.

Keywords

• Sixth-order thin film equation
• radial solution
• existence
• finite speed of propagation