Continuous Dependence for 2×2 Conservation Laws with Boundary
Continuous Dependence for 2×2 Conservation Laws with Boundary
复制标题
有边界的 2×2 守恒定律的连续依赖
DOI：
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发表时间：
1997
期刊：
影响因子：
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通讯作者：
R. Colombo
中科院分区：
文献类型：
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作者：
D. Amadori;R. Colombo
在domain 0。[(t，x）# R：t0和x9（t）]，对于某个边界轮廓9：R [ R.通常，假设（1.1）是严格双曲的，并且每个特征场都是线性退化的或真正非线性的。给出了具有足够小的总变化的初始数据u（0，x）=u（x）。我们考虑沿沿着x=9（t）的两种不同的边界条件，在这两种情况下，我们构造了一个Lipschitzean流，其轨迹是（1.1）的初边值问题的解。因此，我们证明了连续依赖的解决方案后，初始数据，边界条件和边界轮廓。方程（1.1）的Cauchy问题的整体BV解的存在性理论可以追溯到Glimm的基本论文[15]。最近，在[6]中，引入了一种新方法。它依赖于Lipschitzean半群的构造，标准黎曼半群（SRS），其轨迹扩展了黎曼问题的局部标准Lax [17]解。目前，在文献[8，9]中已经在2_2情况下构造了这样的SRS，而对于一般的n_n情况，参见文献DE 973274中的[7，10]和[3
on the domain 0.[(t, x) # R : t 0 and x 9(t)], for some boundary profile 9: R [ R. As usual, (1.1) is assumed to be strictly hyperbolic and with each characteristic field either linearly degenerate or genuinely non linear. An initial data u(0, x)=u (x) having sufficiently small total variation is given. We consider two different kinds of boundary conditions along x=9(t) and in both cases we construct a Lipschitzean flow whose trajectories are solutions of an initial-boundary value problem for (1.1). Thus, we prove the continuous dependence of the solution upon the initial data, upon the boundary condition and upon the boundary profile. The existence theory for global BV solutions to the Cauchy Problem for (1.1) goes back to the fundamental paper [15] by Glimm. More recently, in [6], a new approach has been introduced. It relies on the construction of a Lipschitzean semigroup, the Standard Riemann Semigroup (SRS), whose trajectories extend the local standard Lax [17] solutions of Riemann Problems. At present, such a SRS has been constructed in the 2_2 case in [8, 9], while for the general n_n case see [7, 10] and [3] in article no. DE973274