小粘性非线性发展偏微分方程的临界行为
On critical behavior in nonlinear evolutionary PDEs with small viscosity
摘要：
本文讨论了拟线性迁移方程的一般耗散正则化问题。我们认为正则化方程的解在迁移方程的梯度突变点附近的局部行为可以用Pearcey函数的对数导数来描述，这是A.M.Il'in的结果的推广。我们提供了一些分析参数支持这样的猜想，并测试它的数值。
英文摘要：
We address the problem of general dissipative regularization of the quasilinear transport equation. We argue that the local behavior of solutions to the regularized equation near the point of gradient catastrophe for the transport equation is described by the logarithmic derivative of the Pearcey function, a statement generalizing the result of A.M.Il'in. We provide some analytic arguments supporting such conjecture and test it numerically.
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