1) global weak solution
整体弱解
1.
Existence of global weak solutions to the semiconductor equations with heat effect;
考虑热效应时半导体方程整体弱解的存在性
2.
Using the Galerkin method,the existence of a global weak solution was proven,indicating the solvability of the system and the possibility of numerical solutions.
利用伽辽金方法,得到了整体弱解在某些条件下的存在性,一方面,揭示了这类系统的可解性;另一方面,为数值求解本系统提供了可能。
3.
The Galerkin method,together with the potential well(stable set) method,is employed to solve the existence of global weak solutions of the primary limit value of a kind of semi-linear parabolic equations: in case of high dimension when.
运用Galerkin方法并结合势井理论,证明了一类半线性抛物型方程ut-Δu+up=0的高维情形的初边值混和问题在t 0的整体弱解的存在性。
2) global weakly strong solution
整体弱强解
3) global weak entropy solution
整体弱熵解
1.
Structure of global weak entropy solution for initial-boundary value problems of scalar conservation laws with non-convexity conditions;
具有非凸条件的单个守恒律初边值问题整体弱熵解的结构
2.
Structure of the global weak entropy solution of nonconvex scalar conservation laws with boundary conditions;
具有边界条件的非凸单个守恒律整体弱熵解的结构
3.
By the polygonal approximation method,a global approximation solution is constructed for the initial-boundary value problem of nonconvex scalar conservation laws with two-side boundary effect,and its convergence to the global weak entropy solution of the corresponding problem is proved.
使用折线逼近法,对具有两条边界影响的非凸单个守恒律初边值问题构造了整体近似解,并证明其收敛到初边值问题的整体弱熵解。
4) global weakly discontinuous solution
整体弱间断解
1.
Under the assumption that the inhomogeneous term satisfies the matching condition,we obtain a necessary and sufficient condition to guarantee the existence and uniqueness of global weakly discontinuous solutions to the Cauchy problem with a kind of non-smooth initial data for inhomogeneous quasilinear hyperbolic systems.
在非齐次项满足匹配条件的假设下,得到了此问题存在唯一的整体弱间断解的充要条件。
5) global continuous weak entropy solution
整体连续的弱熵解
1.
This thesis is concerned with the global continuous weak entropy solution and the L~1 convergence rate of its viscosity approximations for the initial-boundary problem of scalar conservation laws.
本文研究单个守恒律初边值问题的整体连续的弱熵解及其粘性逼近解的L~1收敛率。
2.
A sufficient condition that its global continuous weak entropy solution exists and is unique for the initial-boundary problem of scalar convex conservation laws is given,and the global continuous weak entropy solution is constructed by the truncation method,as well as its boundary behaviors is obtained.
对单个凸守恒律的初边值问题给出其整体连续的弱熵解存在且唯一的一个充分条件,并用截断方法构造其整体连续弱熵解,从而得到弱熵解的边界性态。
3.
According to the structure of the global continuous weak entropy solution of the initial-boundary problem of scalar conservation laws, and using L1-stability lemma for nonhomogeneous viscous equations with initial-boundary conditions, This thesis attain a convergence rate that the viscosity solution converge to the inviscid solution in L1-norm.
根据单个守恒律初边值问题的整体连续的弱熵解的结构,利用具有初边值条件的非齐次粘性方程的L1-稳定性引理导出其粘性解L1收敛到无粘解的一个收敛率。
补充资料：弱解
弱解
weak solution
弱解I叭限，kso加‘叨;e顽oe petue。。e] 微分方程 无。三艺a:(x)D“u=f(*) I匡l‘门在区域D的弱解是一局部可积函数u，它对在D中具有紧支集的所有光滑函数毋(比如，C田类函数)满足等式 丁·L‘，“二一丁f，己/. DD这里，(*)中的系数a。(%)假定是充分光滑的，而L’是L的形式的肠脚nge伴随算子: 五‘价一艺(一l)，·，D·(a。毋). l口}《m例如，广义导数f=D““可以定义为局部可积函数f，使得“是方程D‘“”f的一个弱解. 在考虑(*)的弱解时，产生下面的问题:在什么条件下它们是强解(见强解(strong solution))?例如，在椭圆型方程情形下，每一个弱解都是强解.
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参考词条