Abstract :
We study the degenerate parabolic equation utq= ? fs= ? Q=u.qg, where
x, t.gRN =Rq, the flux f, the viscosity coefficient Q, and the source term g
depend on x, t, u. and Q is nonnegative definite. Due to the possible degeneracy,
weak solutions are considered. In general, these solutions are not uniquely determined
by the initial data and, therefore, additional conditions must be imposed in
order to guarantee uniqueness. We consider here the subclass of piecewise smooth
weak solutions, i.e., continuous solutions which are C2-smooth everywhere apart
from a closed nowhere dense collection of smooth manifolds. We show that the
solution operator is L1-stable in this subclass and, consequently, that piecewise
smooth weak solutions are uniquely determined by the initial data.
