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 |
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Pages (from-to) | 415-433 |
Number of pages | 19 |
Journal | Bulletin des Sciences Mathematiques |
Volume | 124 |
Issue number | 5 |
DOIs | |
Publication status | Published - Jul 2000 |
All Science Journal Classification (ASJC) codes
- General Mathematics