On the diffusion phenomenon of quasilinear hyperbolic waves

Journal article

Authors/Editors

Milani, Albert

Research Areas

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Publication Details

Author list: Yang H, Milani A

Publisher: Elsevier

Place: PARIS

Publication year: 2000

Journal: Bulletin des Sciences Mathématiques (0007-4497)

Journal acronym: B SCI MATH

Volume number: 124

Issue number: 5

Start page: 415

End page: 733

Number of pages: 319

ISSN: 0007-4497

Languages: English-Great Britain (EN-GB)

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Abstract

We consider the asymptotic behavior of solutions of the quasilinear hyperbolic equation with linear dampingu(tt) + u(t) - div(a(del u)del u) = 0,and show that they tend, as t --> +infinity, to those of the nonlinear parabolic equationv(t) - div(a(del v)del v) = 0,in the sense that the norm \\ u(.,t) - v(.,t)\\(L infinity(Rn)) Of the difference u - v decays faster than that of either u or v. This provides another example of the diffusion phenomenon of nonlinear hyperbolic waves, first observed by L. Hsiao and Tai-ping Liu. (C) 2000 Editions scientifiques et medicales Elsevier SAS.

Keywords

asymptotic behavior of solutions, diffusion phenomenon, quasilinear hyperbolic and parabolic equations

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