Asymptotics for the Burgers equation with pumping

Nakao Hayashi; Pavel I. Naumkin

doi:10.1007/s00220-003-0876-7

Asymptotics for the Burgers equation with pumping

Nakao Hayashi, Pavel I. Naumkin

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

4 Citations (Scopus)

Abstract

We consider the large time asymptotic behavior of solutions to the initial-boundary value problem { u_t + e^t u u_x - u_xx = 0, x ∈ R, t > 0, u (0, x) = u₀ (x), x ∈ R, u(t, x) → a_±, x → ±∞, t > 0. We find large time asymptotic formulas of solutions for three different cases 1)a_± = ±1, 2)a_± = ∓1 and 3) a_± = 0.

Original language	English
Pages (from-to)	287-307
Number of pages	21
Journal	Communications in Mathematical Physics
Volume	239
Issue number	1-2
DOIs	https://doi.org/10.1007/s00220-003-0876-7
Publication status	Published - 2003 Aug
Externally published	Yes

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/s00220-003-0876-7

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title = "Asymptotics for the Burgers equation with pumping",

abstract = "We consider the large time asymptotic behavior of solutions to the initial-boundary value problem { ut + et u ux - uxx = 0, x ∈ R, t > 0, u (0, x) = u0 (x), x ∈ R, u(t, x) → a±, x → ±∞, t > 0. We find large time asymptotic formulas of solutions for three different cases 1)a± = ±1, 2)a± = ∓1 and 3) a± = 0.",

author = "Nakao Hayashi and Naumkin, {Pavel I.}",

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AU - Naumkin, Pavel I.

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AB - We consider the large time asymptotic behavior of solutions to the initial-boundary value problem { ut + et u ux - uxx = 0, x ∈ R, t > 0, u (0, x) = u0 (x), x ∈ R, u(t, x) → a±, x → ±∞, t > 0. We find large time asymptotic formulas of solutions for three different cases 1)a± = ±1, 2)a± = ∓1 and 3) a± = 0.

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Asymptotics for the Burgers equation with pumping

Abstract

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