摘要
A fourth-order degenerate parabolic equation with a viscous term: ?is studied with the initial-boundary conditions ux=wx=0?on {-1,1}×(0,T), u(x,0)=u0(x)?in (-1,1). It can be taken as a thin film equation or a Cahn-Hilliard equation with a degenerate mobility. The entropy functional method is introduced to overcome the difficulties that arise from the degenerate mobility m(u)?and the viscosity term. The existence of nonnegative weak solution is obtained.
A fourth-order degenerate parabolic equation with a viscous term: ?is studied with the initial-boundary conditions ux=wx=0?on {-1,1}×(0,T), u(x,0)=u0(x)?in (-1,1). It can be taken as a thin film equation or a Cahn-Hilliard equation with a degenerate mobility. The entropy functional method is introduced to overcome the difficulties that arise from the degenerate mobility m(u)?and the viscosity term. The existence of nonnegative weak solution is obtained.
