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| ON THE DIFFUSION PHENOMENON OF QUASILINEAR HYPERBOLICWAVES |
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Citation： |
YANG Han.ON THE DIFFUSION PHENOMENON OF QUASILINEAR HYPERBOLICWAVES[J].Chinese Annals of Mathematics B,2000,21(1):63~70 |
| Page view： 1274
Net amount： 683 |
Authors： |
YANG Han; |
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| Abstract： |
The authors consider the asymptotic behavior of solutions of the quasilinear hyperbolic equation with linear damping $$ u_{tt} + u_t - \hbox{div}\,(a(\nabla u)\nabla u) = 0, $$ and show that, at least when $n\leq 3,$ they tend, as $t \to + \ue$, to those of the nonlinear parabolic equation $$ v_t-\hbox{div}\,(a(\nabla v)\nabla v)=0, $$ in the sense that the norm $\|u(.,t)-v(.,t)\|_{L^{\infty}(\rn)}$ 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]). |
Keywords： |
Asymptotic behavior of solutions, Quasilinear hyperbolic and parabolic equations, Diffusion phenomenon |
Classification： |
35B40, 35L70 |
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