Remarks on a Nonlinear Parabolic Equation.

Matania Ben-Artzi, Jonathan Goodman, Arnon Levy

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


The equation $u_{t} =\Delta u +\mu |\nabla u | $, $\mu \in \mathbb{R}$, is studied in $\mathbb{R}^{n}$ and in the periodic case. It is shown that the equation is well-posed in $L^{1}$ and possesses regularizing properties. For nonnegative initial data and $\mu <0$ the solution decays in $L^{1}(\mathbb{R}^{n})$ as $t\to \infty $. 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
Pages (from-to)731-751
Number of pages21
JournalTransactions of the American Mathematical Society
Issue number2
StatePublished - 1 Feb 2000


  • PERIODIC functions


Dive into the research topics of 'Remarks on a Nonlinear Parabolic Equation.'. Together they form a unique fingerprint.

Cite this