论文标题
汉密尔顿 - 雅各比方程与ra量度值的标量保护法的不连续解决方案：奇异性的消失
Discontinuous solutions of Hamilton-Jacobi equations versus Radon measure-valued solutions of scalar conservation laws: Disappearance of singularities
论文作者
论文摘要
令$ h $为有限的Lipschitz连续功能。我们考虑汉密尔顿 - 雅各比方程的不连续粘度解决方案$ u_ {t}+h（u_x）= 0 $和签名的radon测量估计熵解决方案$ u_ {t}+[t}+[h（u）] _ x = 0 $。在证明了正式关系$ u_x = u $的确切陈述之后，我们建立了（严格为正面！）时间的估算值，在该时间中，解决方案的奇异性消失了。在这里，在汉密尔顿 - 雅各比方程式中，奇异性是跳跃不连续性，并且在保护法的情况下签署了奇异措施。
Let $H$ be a bounded and Lipschitz continuous function. We consider discontinuous viscosity solutions of the Hamilton-Jacobi equation $U_{t}+H(U_x)=0$ and signed Radon measure valued entropy solutions of the conservation law $u_{t}+[H(u)]_x=0$. After having proved a precise statement of the formal relation $U_x=u$, we establish estimates for the (strictly positive!) times at which singularities of the solutions disappear. Here singularities are jump discontinuities in case of the Hamilton-Jacobi equation and signed singular measures in case of the conservation law.
