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 language | English |
|---|---|
| Pages (from-to) | 415-433 |
| Number of pages | 19 |
| Journal | Bulletin des Sciences Mathematiques |
| Volume | 124 |
| Issue number | 5 |
| DOIs | |
| Publication status | Published - Jan 1 2000 |
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All Science Journal Classification (ASJC) codes
- Mathematics(all)
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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 journal › Article
TY - JOUR
T1 - On the diffusion phenomenonof quasilinear hyperbolic waves
AU - Yang, Han
AU - Milani, Albert
PY - 2000/1/1
Y1 - 2000/1/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0000261756&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0000261756&partnerID=8YFLogxK
U2 - 10.1016/S0007-4497(00)00141-X
DO - 10.1016/S0007-4497(00)00141-X
M3 - Article
AN - SCOPUS:0000261756
VL - 124
SP - 415
EP - 433
JO - Bulletin des Sciences Mathematiques
JF - Bulletin des Sciences Mathematiques
SN - 0007-4497
IS - 5
ER -