论文标题
标量保护法的最小熵条件，具有一般凸通量
Minimal Entropy Conditions for Scalar Conservation Laws with General Convex Fluxes
论文作者
论文摘要
我们关注具有一般凸通量函数的一维标量保护定律的最小熵条件。对于这样的标量保护法，我们证明了一个单个熵 - 内部通量对$（η（u），q（u），q（u））$，$η（u）$严格的凸度足以在$ l^\ infty _ {\ rm rm loc}中的广泛弱解决方案中挑出一个较弱的弱解决方案。对于某些非负ra量$μ$的分布意义上的μ$。此外，我们将此结果扩展到$ l^p _ {\ rm loc} $中的弱解决方案类别，基于Flux函数的渐近行为$ f（u）$和Infinity的熵函数$η（u）$。这些证明是基于一维标量保护定律的熵解决方案与相应的汉密尔顿 - 雅各比方程的粘度解，双线性形式和换向因子估计的粘度解之间的等效性。
We are concerned with the minimal entropy conditions for one-dimensional scalar conservation laws with general convex flux functions. For such scalar conservation laws, we prove that a single entropy-entropy flux pair $(η(u),q(u))$ with $η(u)$ of strict convexity is sufficient to single out an entropy solution from a broad class of weak solutions in $L^\infty_{\rm loc}$ that satisfy the inequality: $η(u)_t+q(u)_x\leq μ$ in the distributional sense for some non-negative Radon measure $μ$. Furthermore, we extend this result to the class of weak solutions in $L^p_{\rm loc}$, based on the asymptotic behavior of the flux function $f(u)$ and the entropy function $η(u)$ at infinity. The proofs are based on the equivalence between the entropy solutions of one-dimensional scalar conservation laws and the viscosity solutions of the corresponding Hamilton-Jacobi equations, as well as the bilinear form and commutator estimates as employed similarly in the theory of compensated compactness.
