Remarks on a nonlinear parabolic equation

Matania Ben-Artzi, Jonathan Goodman, Arnon Levy

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish (US)
Pages (from-to)731-751
Number of pages21
JournalTransactions of the American Mathematical Society
Volume352
Issue number2
DOIs
StatePublished - 2000

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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