### 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 language | English (US) |
---|---|

Pages (from-to) | 731-751 |

Number of pages | 21 |

Journal | Transactions of the American Mathematical Society |

Volume | 352 |

Issue number | 2 |

State | Published - 2000 |

### Fingerprint

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Transactions of the American Mathematical Society*,

*352*(2), 731-751.

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

Research output: Contribution to journal › Article

*Transactions of the American Mathematical Society*, vol. 352, no. 2, pp. 731-751.

}

TY - JOUR

T1 - Remarks on a nonlinear parabolic equation

AU - Ben-Artzi, Matania

AU - Goodman, Jonathan

AU - Levy, Arnon

PY - 2000

Y1 - 2000

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=22844456168&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=22844456168&partnerID=8YFLogxK

M3 - Article

VL - 352

SP - 731

EP - 751

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 2

ER -