The equation ut = Δu + μ|∇u|, μ ∈ ℝ, is studied in ℝn and in the periodic case. It is shown that the equation is well-posed in L1 and possesses regularizing properties. For nonnegative initial data and μ < 0 the solution decays in L1(ℝn) as t → ∞. In the periodic case it tends uniformly to a limit. A consistent difference scheme is presented and proved to be stable and convergent.
ASJC Scopus subject areas
- Applied Mathematics