Remarks on a nonlinear parabolic equation

Matania Ben-Artzi; Jonathan Goodman; Arnon Levy

doi:10.1090/s0002-9947-99-02336-3

Remarks on a nonlinear parabolic equation

Matania Ben-Artzi, Jonathan Goodman, Arnon Levy

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

The equation u_t = 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 language	English (US)
Pages (from-to)	731-751
Number of pages	21
Journal	Transactions of the American Mathematical Society
Volume	352
Issue number	2
DOIs	https://doi.org/10.1090/s0002-9947-99-02336-3
State	Published - 2000

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1090/s0002-9947-99-02336-3

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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.",

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AB - 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.

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Remarks on a nonlinear parabolic equation

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