Remarks on a nonlinear parabolic equation

The equation u(t) = Delta u + mu\del u\, mu is an element of R, is studied in R-n and in the periodic case. It is shown that the equation is well-pose d in L-1 and possesses regularizing properties. For nonnegative initial dat a and mu < 0 the solution decays in L-1 (R-n) as t --> infinity. In the per iodic case it tends uniformly to a limit. A consistent difference scheme is presented and proved to be stable and convergent.