Polygonal approximations of solutions of the initial value problem for a conservation law
Polygonal approximations of solutions of the initial value problem for a conservation law
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DOI：
10.1016/0022-247x(72)90114-x
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发表时间：
1972-04
影响因子：
1.3
通讯作者：
C. Dafermos
中科院分区：
文献类型：
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作者：
C. Dafermos
本文介绍了研究初值问题的一种新方法，其中f（u）是局部Lipschitz连续的，U_1，（X）是有界的，且是（-CO，m）上的局部有界变差的.一般地，即使f和U_1是光滑的，（1.1）和（1.2）也不存在经典解.已经证明了用粘性消失[1]、有限差分[2]和光滑化[3]的方法来建立弱解的存在性是可能的。L
In this article we introduce a new method for the study of the initial value problem wheref (u) is locally Lipschitz continuous and U,,(X) is bounded and of locally bounded variation on (-CO, m).In general no classical solution of (1.1) and (1.2) exists even if f and u,, are smooth. It has been demonstrated that it is possible to establish the existence of weak solutions by the methods of vanishing viscosity [l] finite differences [2] and smoothing [3]. l