Γ -Entropy Cost for Scalar Conservation Laws
Γ -Entropy Cost for Scalar Conservation Laws
复制标题
Г - 标量守恒定律的熵成本
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
M. Novaga
中科院分区：
文献类型：
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作者：
G. Bellettini;L. Bertini;M. Mariani;M. Novaga
本文研究了标量守恒律的粘性消失近似的控制问题。当粘性系数趋于零时，我们研究了控制代价泛函的Γ -收敛性。建立了一个一阶Γ -极限，它将守恒律的测度值解刻画为Γ -极限的零点.然后研究了二阶Γ -极限，给出了守恒律熵解作为Γ -极限零点的一个特征.
We are concerned with a control problem related to the vanishing viscosity approximation to scalar conservation laws. We investigate the Γ -convergence of the control cost functional, as the viscosity coefficient tends to zero. A first-order Γ -limit is established, which characterizes the measure-valued solutions to the conservation laws as the zeros of the Γ -limit. A second-order Γ -limit is then investigated, providing a characterization of entropic solutions to conservation laws as the zeros of the Γ -limit.