Remarks on a nonlinear parabolic equation

Matania Ben-Artzi, Jonathan Goodman, Arnon Levy

Research output: Contribution to journalArticle

Abstract

The equation u t = Δu + μ|∇u|, μ ∈ ℝ, is studied in 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 μ < 0 the solution decays in L 1(ℝ n) 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
StatePublished - 2000

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Nonlinear Parabolic Equations
Difference Scheme
Non-negative
Decay
Tend

ASJC Scopus subject areas

  • Mathematics(all)

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Ben-Artzi, M., Goodman, J., & Levy, A. (2000). Remarks on a nonlinear parabolic equation. Transactions of the American Mathematical Society, 352(2), 731-751.

Remarks on a nonlinear parabolic equation. / Ben-Artzi, Matania; Goodman, Jonathan; Levy, Arnon.

In: Transactions of the American Mathematical Society, Vol. 352, No. 2, 2000, p. 731-751.

Research output: Contribution to journalArticle

Ben-Artzi, M, Goodman, J & Levy, A 2000, 'Remarks on a nonlinear parabolic equation', Transactions of the American Mathematical Society, vol. 352, no. 2, pp. 731-751.
Ben-Artzi, Matania ; Goodman, Jonathan ; Levy, Arnon. / Remarks on a nonlinear parabolic equation. In: Transactions of the American Mathematical Society. 2000 ; Vol. 352, No. 2. pp. 731-751.
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