Long‐time diffusive behavior of solutions to a hyperbolic relaxation system
Long‐time diffusive behavior of solutions to a hyperbolic relaxation system
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双曲松弛系统解的长期扩散行为
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发表时间：
2001
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通讯作者：
R. Natalini
中科院分区：
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作者：
Hailiang Liu;R. Natalini
研究了具有弛豫源ut+vx=0，vt+aUx=f(U)−v，(x，t)∈R×R，初值(u，v)=(u0，v0)，u0，v0∈L(R)∩L∞(R)，f(U)=αu/2和|v0|6 au0的系统柯西问题解的大时间性态。在次特征条件下，证明了当t→∞时，u以比t−(p−1)/2p更快的速度趋于对流扩散方程ut+f(U)x=auxx在L范数下的基本解.
We study the large time behavior of the solutions to the Cauchy problem for the system with relaxation source ut + vx = 0, vt + a ux = f (u) − v, with (x, t) ∈ R × R, for the initial data (u, v) = (u0, v0) at t = 0, with u0, v0 ∈ L(R) ∩ L∞(R), f (u) = αu/2 and |v0| 6 au0. Under the sub-characteristic condition we show that, as t → ∞, the component u tends towards a fundamental solution of the convection-diffusion equation ut + f (u)x = a uxx in the L norm, at a rate faster than t−(p−1)/2p.