AI 中文总结
研究通过前沿追踪格式证明p - 系统弱解存在性，确定无穷多波前条件，针对通量低正则性提出新方法获相互作用估计，证明解的稳定性并得出从分段仿射通量到光滑通量的解的收敛速度。
AI 中文摘要
我们证明了具有分段仿射通量函数的p - 系统全局弱熵解的存在性。该构造基于波前追踪格式，为此我们确定了无穷多个波前出现的充要条件。对于光滑通量，理论已完善。但通量的低Lipschitz正则性需要新方法来获得相互作用估计。我们还在文献[bia - col - 02]的意义下证明了解的稳定性，表明解关于通量导数差的\(L^{\infty}\)范数是Lipschitz连续的。利用稳定性估计得到了从分段仿射通量到光滑通量的解的收敛速度。
英文摘要
We prove the existence of global weak entropy solutions to the $p$-system with the piecewise affine flux function. The construction is based on a wave-front tracking scheme for which we identify a necessary and sufficient condition for the occurrence of infinitely many fronts. For smooth fluxes, the theory is well established. However, the lower Lipschitz regularity of the flux requires a new method to obtain the interaction estimates. We also prove the stability of the solution in the sense of \cite{bia-col-02}, showing that solutions are Lipschitz continuous with respect to the $L^{\infty}$ norm of the difference of the flux derivatives. We obtain the convergence rate of the solutions from the piecewise affine flux to smooth flux by using the stability estimate.
