On the diffusion phenomenonof quasilinear hyperbolic waves

Han Yang, Albert Milani

Research output: Contribution to journalArticlepeer-review

79 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 - Jul 2000

All Science Journal Classification (ASJC) codes

  • General Mathematics

Fingerprint

Dive into the research topics of 'On the diffusion phenomenonof quasilinear hyperbolic waves'. Together they form a unique fingerprint.

Cite this