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On the diffusion phenomenonof quasilinear hyperbolic waves

✍ Scribed by Han Yang; Albert Milani

Book ID
104106117
Publisher
Elsevier Science
Year
2000
Tongue
French
Weight
109 KB
Volume
124
Category
Article
ISSN
0007-4497

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✦ Synopsis

We consider the asymptotic behavior of solutions of the quasilinear hyperbolic equation with linear damping u tt + u tdiv(a(βˆ‡u)βˆ‡u) = 0, and show that they tend, as t β†’ +∞, to those of the nonlinear parabolic equation v tdiv(a(βˆ‡v)βˆ‡v) = 0, in the sense that the norm u(. , t)v(. , t) L ∞ (R n ) of the difference uv 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.

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