Long-time behavior for a nonlinear fourth-order parabolic equation

María J. Cáceres; J. A. Carrillo; G. Toscani

doi:10.1090/S0002-9947-04-03528-7

Long-time behavior for a nonlinear fourth-order parabolic equation

María J. Cáceres, J. A. Carrillo, G. Toscani

Departament de Matemàtiques

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We study the asymptotic behavior of solutions of the initial-boundary value problem, with periodic boundary conditions, for a fourth-order nonlinear degenerate diffusion equation with a logarithmic nonlinearity. For strictly positive and suitably small initial data we show that a positive solution exponentially approaches its mean as time tends to infinity. These results are derived by analyzing the equation verified by the logarithm of the solution. © 2004 American Mathematical Society.

Idioma original	Anglès
Pàgines (de-a)	1161-1175
Revista	Transactions of the American Mathematical Society
Volum	357
DOIs	https://doi.org/10.1090/S0002-9947-04-03528-7
Estat de la publicació	Publicada - 1 de març 2005

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10.1090/S0002-9947-04-03528-7

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title = "Long-time behavior for a nonlinear fourth-order parabolic equation",

abstract = "We study the asymptotic behavior of solutions of the initial-boundary value problem, with periodic boundary conditions, for a fourth-order nonlinear degenerate diffusion equation with a logarithmic nonlinearity. For strictly positive and suitably small initial data we show that a positive solution exponentially approaches its mean as time tends to infinity. These results are derived by analyzing the equation verified by the logarithm of the solution. {\textcopyright} 2004 American Mathematical Society.",

keywords = "Asymptotic behavior, Degenerate parabolic equation, Diffusion equation, Entropy dissipation",

author = "C{\'a}ceres, {Mar{\'i}a J.} and Carrillo, {J. A.} and G. Toscani",

year = "2005",

month = mar,

day = "1",

doi = "10.1090/S0002-9947-04-03528-7",

language = "English",

volume = "357",

pages = "1161--1175",

journal = "Transactions of the American Mathematical Society",

issn = "0002-9947",

publisher = "American Mathematical Society",

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T1 - Long-time behavior for a nonlinear fourth-order parabolic equation

AU - Cáceres, María J.

AU - Carrillo, J. A.

AU - Toscani, G.

PY - 2005/3/1

Y1 - 2005/3/1

N2 - We study the asymptotic behavior of solutions of the initial-boundary value problem, with periodic boundary conditions, for a fourth-order nonlinear degenerate diffusion equation with a logarithmic nonlinearity. For strictly positive and suitably small initial data we show that a positive solution exponentially approaches its mean as time tends to infinity. These results are derived by analyzing the equation verified by the logarithm of the solution. © 2004 American Mathematical Society.

AB - We study the asymptotic behavior of solutions of the initial-boundary value problem, with periodic boundary conditions, for a fourth-order nonlinear degenerate diffusion equation with a logarithmic nonlinearity. For strictly positive and suitably small initial data we show that a positive solution exponentially approaches its mean as time tends to infinity. These results are derived by analyzing the equation verified by the logarithm of the solution. © 2004 American Mathematical Society.

KW - Asymptotic behavior

KW - Degenerate parabolic equation

KW - Diffusion equation

KW - Entropy dissipation

U2 - 10.1090/S0002-9947-04-03528-7

DO - 10.1090/S0002-9947-04-03528-7

M3 - Article

SN - 0002-9947

VL - 357

SP - 1161

EP - 1175

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

ER -

Long-time behavior for a nonlinear fourth-order parabolic equation

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