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 |
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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 |
All Science Journal Classification (ASJC) codes
- Mathematics(all)
- Applied Mathematics