Radial symmetric solutions of the Cahn-Hilliard equation with degenerate mobility (Q2718890)

The authors consider an initial-boundary value problem for the Cahn-Hilliard equation NEWLINE\[NEWLINE{\partial u\over\partial t}+ \text{div}[m(u)(k\nabla\Delta u-\nabla A(u))]= 0NEWLINE\]NEWLINE with nonconstant mobility, which can also degenerate. They focus on a case when the domain is the two-dimensional unit ball and study the weak radially symmetric solutions. The existence of such solutions is obtained via passing to a limit in a sequence of solutions to the regularized `radial symmetric' problem. In the final section the authors show that a weak radially symmetric solution stays nonnegative if the initial condition is nonnegative.