On the diffusion phenomenonof quasilinear hyperbolic waves

Han Yang, Albert Milani

Research output: Contribution to journalArticle

69 Citations (Scopus)

Abstract

We consider the asymptotic behavior of solutions of the quasilinear hyperbolic equation with linear damping utt+ut-div(a(∇u)∇u)=0, and show that they tend, as t→+∞, to those of the nonlinear parabolic equation vt-div(a(∇v)∇v)=0, in the sense that the norm u(.,t)-v(.,t)L∞(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.

Original languageEnglish
Pages (from-to)415-433
Number of pages19
JournalBulletin des Sciences Mathematiques
Volume124
Issue number5
DOIs
Publication statusPublished - Jan 1 2000

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Quasilinear Hyperbolic Equation
Nonlinear Parabolic Equations
Asymptotic Behavior of Solutions
Damping
Decay
Tend
Norm

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

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On the diffusion phenomenonof quasilinear hyperbolic waves. / Yang, Han; Milani, Albert.

In: Bulletin des Sciences Mathematiques, Vol. 124, No. 5, 01.01.2000, p. 415-433.

Research output: Contribution to journalArticle

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