Oleinik Type Estimates and Uniqueness for n×n Conservation Laws
Oleinik Type Estimates and Uniqueness for n×n Conservation Laws
复制标题
n×n 守恒定律的 Oleinik 类型估计和唯一性
DOI：
10.1006/jdeq.1998.3606
复制
发表时间：
1999
影响因子：
2.4
通讯作者：
P. Goatin
中科院分区：
文献类型：
--
作者：
A. Bressan;P. Goatin
设ut+f（u）x=0是一维严格双曲n×n守恒律组。依靠解的半群的存在性，我们首先建立了Cauchy问题的熵容许弱解的唯一性，并在t-x平面上每一点的前向邻域中对u的局部振动作了一个温和的假设.反过来，这产生的唯一性弱解满足衰减估计的正波真正的非线性家庭，从而扩展了经典的结果证明了Oleinik在标量的情况下。
Abstract Let ut+f(u)x=0 be a strictly hyperbolic n×n system of conservation laws in one space dimension. Relying on the existence of a semigroup of solutions, we first establish the uniqueness of entropy admissible weak solutions to the Cauchy problem, under a mild assumption on the local oscillation of u in a forward neighborhood of each point in the t-x plane. In turn, this yields the uniqueness of weak solutions which satisfy a decay estimate on positive waves of genuinely nonlinear families, thus extending a classical result proved by Oleinik in the scalar case.