非自治退化抛物-双曲方程的柯西问题

Cauchy Problem for Non-autonomous Degenerate Parabolic-Hyperbolic Equations

非自治退化抛物-双曲型方程可以描述许多自然现象.主要研究这类方程的柯西问题,建立了动力学公式,在对流函数、扩散函数适当光滑性的基础上,证明了该问题动力学解的存在唯一性.

Non-autonomous degenerate parabolic-hyperbolic equations can be used to describe many physical phenomena. The paper is mainly concerned with the Cauchy problem for this kind of equations. The kinetic formulation is constructed. Under suitable smooth conditions for the flux and diffusion function, the existence and uniqueness of kinetic solutions for the Cauchy problem is obtained.