论文标题
冲击波动力学的小分散近似
Small dispersion approximation of shock wave dynamics
论文作者
论文摘要
我们使用各种动力学表示，引入了多维标量保护定律的弱熵溶液的分散近似，其中平衡密度满足GIBB的熵最小化原理，用于分段线性，凸熵。对于这样的解决方案，我们表明，通过熵增量来衡量的小规模不连续性以特征性的速度传播，而大规模的冲击型不连续性则以接近经典冲击波速度的速度传播。在比例参数的零限制中，近似解决方案会收敛到标量保护定律的独特的熵解决方案。
We introduce a dispersion approximation of weak, entropy solutions of multidimensional scalar conservation laws using variational kinetic representation, where equilibrium densities satisfy the Gibb's entropy minimization principle for a piecewise linear, convex entropy. For such solutions, we show that small scale discontinuities, measured by the entropy increments, propagate with characteristic velocities, while the large scale, shock-type discontinuities propagate with speeds close to the speeds of classical shock waves. In the zero-limit of the scale parameter, approximate solutions converge to a unique, entropy solution of a scalar conservation law.
