Abstract
The authors consider the asymptotic behavior of solutions of the quasilinear hyperbolic equation with linear damping Utt + ut -div (a(∇u) ∇u) = 0, and show that, at least when n ≤ 3, 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 Hsiao, L. and Liu Taiping (see [1, 2]).
| Original language | English |
|---|---|
| Pages (from-to) | 63-70 |
| Number of pages | 8 |
| Journal | Chinese Annals of Mathematics. Series B |
| Volume | 21 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2000 |
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All Science Journal Classification (ASJC) codes
- Mathematics(all)
- Applied Mathematics
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On the diffusion phenomenon of quasilinear hyperbolic waves. / Yang, Han; Milani, Albert.
In: Chinese Annals of Mathematics. Series B, Vol. 21, No. 1, 2000, p. 63-70.Research output: Contribution to journal › Article
TY - JOUR
T1 - On the diffusion phenomenon of quasilinear hyperbolic waves
AU - Yang, Han
AU - Milani, Albert
PY - 2000
Y1 - 2000
N2 - The authors consider the asymptotic behavior of solutions of the quasilinear hyperbolic equation with linear damping Utt + ut -div (a(∇u) ∇u) = 0, and show that, at least when n ≤ 3, 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 Hsiao, L. and Liu Taiping (see [1, 2]).
AB - The authors consider the asymptotic behavior of solutions of the quasilinear hyperbolic equation with linear damping Utt + ut -div (a(∇u) ∇u) = 0, and show that, at least when n ≤ 3, 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 Hsiao, L. and Liu Taiping (see [1, 2]).
UR - http://www.scopus.com/inward/record.url?scp=51649163984&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=51649163984&partnerID=8YFLogxK
U2 - 10.1007/BF02731959
DO - 10.1007/BF02731959
M3 - Article
VL - 21
SP - 63
EP - 70
JO - Chinese Annals of Mathematics. Series B
JF - Chinese Annals of Mathematics. Series B
SN - 0252-9599
IS - 1
ER -