GLOBALLY DEFINED CLASSICAL SOLUTIONS TO FREE BOUNDARY PROBLEMS WITH CHARACTERISTIC BOUNDARY FOR QUASILINEAR HYPERBOLIC SYSTEMS

In this paper, the authors prove the global existence and uniqueness of classical solutions to some free boundary problems with characteristic boundary for the reducible quasilinear hyperbolic system.     

带内部耗散项的拟线性双曲型方程组的柯西问题

§1引言 对常系数常微分方程组的初值问题{其中x(t)是n维向量函数,A是n阶常数矩阵,由常微分方程理论知道,若A的特征值的实部均为非负,且关于实部为零的特征值所对应的初等因子是单重的,则(1.1)的解x(t)必是有界的。如果方程组(1.1)的右端还含未知函数的非线性项,即考虑初值问题     

拟线性双曲型方程组典型自由边界问题的整体经典解

本文对拟线性双曲组的某些典型边值问题及典型自由边界问题,证明了整体经典解的存在唯一性。     

一阶拟线性双曲型方程组的边值问题

本文研究一阶拟线性双曲型方程组在角状区域上的典型边值问题,改进了[1—6]中的结果,即将C~1解的局部可解性条件‖Θ‖min<1放宽到‖Θ_1‖min<1,到且说明了一般地这个条件不能少,并给出了一个局部C~1解不存在的例子。最后,将此结果应用到其它边值问题,且对气体动力学中一维不定常非等熵流方程组的不连续初值问题给出一个应用。     

GLOBAL EXISTENCE OF CLASSICAL SOLUTIONS TO THE TYPICAL FREE BOUNDARY PROBLEM FOR GERENAL QUASILINEAR HYPERBOLIC SYSTEMS AND ITS APPLICATIONS

In this paper the authors prove the existence and uniqueness of global classicalsolutions to the typical free boundary problem for general quasilinear hyperbolic systems.As an application,a unique global discontinuous solution only containing n shocks ont≥0 is obtained for a class of generalized Riemann problem for the quasilinear hyperbolicsystem of n conservation laws.     

Global Exisienoe of Classical Solutions to the Typical Free Boundary Problem for General Quasilinear Hyperbolic Systems and Its Applications

In this paper the authors prove the existence and uniqueness of global classical solutions to the typical free boundary problem for general quasilinear hyperbolic systems. As an application, a unique global discontinuous solution only containing n shocks on t \leq 0 is obtained for a class of generalized Riemann problem for the quasilinear hyperbolic system of n conservation laws.     

一维等熵流气体力学方程组的真空问题

§1 引言对一阶拟线性双曲型方程组(?)的柯酉问题t=0,r=r_0(x),s=s_0(x)(-∞相似文献   

一阶拟线性双曲型方程组的解的正规性

本文考虑一阶拟线性双曲型方程组的柯西问题、角状区域上的典型边值问题以及混合初边值问题,得到了这些问题解的正规性定理,即若这些问题已经有了一个C~1解,且方程组的系数和初值或边值属于C~N(N>1),则这些问题的解也是C~N解,对线性双曲型方程组在角状区域上的线性边值问题,在||?_1}}_(mtn)<1条件下,证明了它的整体光滑解的存在和唯一性。