difference boundary value problem
- difference boundary value problem的基本解释
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差分边值问题
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Compared with the initial value problems of scalar conservation laws with smooth flux function, the global weak entropy solutions for the initial-boundary value problems of scalar conservation laws with weak discontinuous flux function include the following new interaction types: a rarefaction wave collides with the boundary and is absorbed compltetely or partially by the boundary; a rarefaction wave collides with the boundary and the boundary will reflect a contact or non-contact shock wave; a contact or non-contact shock wave collides with the boundary and is absorbed by the boundary; a contact or non-contact shock wave collides with the boundary and a new non-contact shock will rebound from the boundary simultaneously or later.
与具有光滑流函数的单个守恒律的初始值问题相比,具有弱间断流函数的单个守恒律初边值问题的整体弱熵解中包括下列新的相互作用类型:稀疏波碰到边界并被边界部分或全部吸收;稀疏波与边界相撞,边界反射出一个接触或非接触激波;接触或非接触激波碰到边界并被边界吸收;接触或非接触激波与边界相撞,边界同时或稍后反射出一个新的非接触激波。
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For the Riemann boundary value problems for the first order elliptic systems , we translates them to equivalent singular integral equations and proves the existence of the solution to the discussed problems under some assumptions by means of generalized analytic function theory , singular integral equation theory , contract principle or generaliezed contract principle ; For the Riemann-Hilbert boundary value problems for the first order elliptic systems , we proves the problems solvable under some assumptions by means of generalized analytic function theory , Cauchy integral formula , function theoretic approaches and fixed point theorem ; the boundary element method for the Riemann-Hilbert boundary value problems for the generalized analytic function , we obtains the boundary integral equations by means of the generalized Cauchy integral formula of the generalized analytic function , introducing Cauchy principal value integration , dispersing the boundary of the area , and we obtains the solution to the problems using the boundary conditions .
对于一阶椭圆型方程组的Riemann边值问题,是通过把它们转化为与原问题等价的奇异积分方程,利用广义解析函数理论、奇异积分方程理论、压缩原理或广义压缩原理,证明在某些假设条件下所讨论问题的解的存在性;对于一阶椭圆型方程组的Riemann-Hilbert边值问题,利用广义解析函数理论、Cauchy积分公式、函数论方法和不动点原理,证明在某些假设条件下所讨论问题的可解性;广义解析函数的Riemann-Hilbert边值问题的边界元方法是利用广义解析函数的广义Cauchy积分公式,引入Cauchy主值积分,通过对区域边界的离散化,得到边界积分方程,再利用边界条件得到问题的解。
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With the help of the fundamental theory to singular measure differential system, Green's function matrix expression of solution and well-posed boundary condition are given, together with discussing the properties of the Green's function matrix under the influence of impulsive effect In section 5, based on Lyapunov function method, we investigate that the existence of the first boundary value problem to second-order singular system by macthing the solutions to the second boundary value problem; and the existence and uniqueness of three-point boundary value problem to third order singular system by macthing the solutions to two-piont boundary value problem.
第五部分借助Lyapunov函数法,通过将第二类边值问题的解对结成第一类边值问题的解,得到了二阶广义系统的第一类边值问题解的存在性;通过将两点边值问题的解对结成三点边值问题的解,得到了三阶广义系统的三点边值问题解的存在性和唯一性。
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difference boundary value problem:差分边值问题
difference 差 | difference boundary value problem 差分边值问题 | difference differential equation 差分微分方程