Large time decay of solutions to Burgers type equations

Nakao Hayashi; Naoko Ito; Elena I. Kaikina; Pavel I. Naumkin

doi:10.1080/00036810500047493

Large time decay of solutions to Burgers type equations

Nakao Hayashi, Naoko Ito, Elena I. Kaikina, Pavel I. Naumkin

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

2 Citations (Scopus)

Abstract

We study the initial value problem for the nonlinear dissipative equations (Formula presented.) where a ∈ R ⁿ , ρ > 1, σ > 0. We prove that if (Formula presented.) and (Formula presented.) then in the case σ = (ρ − 1)/(n + 1) solutions exist globally and decay as (Formula presented.) And in the case 0 < σ < (ρ − 1)/(n + 1), σ is close to (ρ − 1)/(n + 1), solutions have estimates (Formula presented.).

Original language	English
Pages (from-to)	1005-1024
Number of pages	20
Journal	International Journal of Phytoremediation
Volume	84
Issue number	10
DOIs	https://doi.org/10.1080/00036810500047493
Publication status	Published - 2005 Sept
Externally published	Yes

Keywords

1991 Mathematics Subject Classifications: Primary 35Q35
Burgers type equation
Dissipative nonlinear evolution equation
Large time asymptotics

ASJC Scopus subject areas

Environmental Chemistry
Pollution
Plant Science

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10.1080/00036810500047493

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title = "Large time decay of solutions to Burgers type equations",

abstract = " We study the initial value problem for the nonlinear dissipative equations (Formula presented.) where a ∈ R n , ρ > 1, σ > 0. We prove that if (Formula presented.) and (Formula presented.) then in the case σ = (ρ − 1)/(n + 1) solutions exist globally and decay as (Formula presented.) And in the case 0 < σ < (ρ − 1)/(n + 1), σ is close to (ρ − 1)/(n + 1), solutions have estimates (Formula presented.).",

keywords = "1991 Mathematics Subject Classifications: Primary 35Q35, Burgers type equation, Dissipative nonlinear evolution equation, Large time asymptotics",

author = "Nakao Hayashi and Naoko Ito and Kaikina, {Elena I.} and Naumkin, {Pavel I.}",

year = "2005",

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language = "English",

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T1 - Large time decay of solutions to Burgers type equations

AU - Hayashi, Nakao

AU - Ito, Naoko

AU - Kaikina, Elena I.

AU - Naumkin, Pavel I.

PY - 2005/9

Y1 - 2005/9

N2 - We study the initial value problem for the nonlinear dissipative equations (Formula presented.) where a ∈ R n , ρ > 1, σ > 0. We prove that if (Formula presented.) and (Formula presented.) then in the case σ = (ρ − 1)/(n + 1) solutions exist globally and decay as (Formula presented.) And in the case 0 < σ < (ρ − 1)/(n + 1), σ is close to (ρ − 1)/(n + 1), solutions have estimates (Formula presented.).

AB - We study the initial value problem for the nonlinear dissipative equations (Formula presented.) where a ∈ R n , ρ > 1, σ > 0. We prove that if (Formula presented.) and (Formula presented.) then in the case σ = (ρ − 1)/(n + 1) solutions exist globally and decay as (Formula presented.) And in the case 0 < σ < (ρ − 1)/(n + 1), σ is close to (ρ − 1)/(n + 1), solutions have estimates (Formula presented.).

KW - 1991 Mathematics Subject Classifications: Primary 35Q35

KW - Burgers type equation

KW - Dissipative nonlinear evolution equation

KW - Large time asymptotics

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DO - 10.1080/00036810500047493

M3 - Article

AN - SCOPUS:33748942629

SN - 1522-6514

VL - 84

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EP - 1024

JO - International Journal of Phytoremediation

JF - International Journal of Phytoremediation

IS - 10

ER -

Large time decay of solutions to Burgers type equations

Abstract

Keywords

ASJC Scopus subject areas

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