Initial propagation of support in thin-film flow

Abstract

We study the behaviour for small time of interfaces connected with supports of strong solutions of one-dimensional thin-film equation with compactly supported initial functions. In some sense, sharp upper estimates of interfaces are obtained for initial functions with arbitrary asymptotic behaviour near the boundary of their supports.

Keywords:

• thin-film equation
• compactly supported initial function
• strong solution
• finite speed propagation
• initial behaviour of interface

AMS Subject Classifications:

• 35B40
• 35K65

View correction statement:

Erratum

Notes

Dedicated to Professor Alexander Pankov on the occasion of his 65th birthday.