A quantitative compactness estimate for scalar conservation laws
A quantitative compactness estimate for scalar conservation laws
复制标题
标量守恒定律的定量紧致性估计
DOI：
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
F. Golse
中科院分区：
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作者：
Camillo De Lellis;F. Golse
在一维空间中，P. D。Lax证明了[Comm. Pure and Appl. Math.7（1954）]定义熵解的半群在L loc 1中对每个正时间是紧的。本说明给出了时间t > 0时熵解集L loc 1中的ε-熵的估计，其初始数据穿过L1中的有界集。© 2005 Wiley Periodicals，Inc.
In the case of a scalar conservation law with convex flux in space dimension one, P. D. Lax proved [Comm. Pure and Appl. Math. 7 (1954)] that the semigroup defining the entropy solution is compact in L loc1 for each positive time. The present note gives an estimate of the ϵ‐entropy in L loc1 of the set of entropy solutions at time t > 0 whose initial data run through a bounded set in L1. © 2005 Wiley Periodicals, Inc.