【作者】 霍平；

【导师】 刘红霞；

【作者基本信息】 暨南大学 ， 基础数学， 2003， 硕士

【摘要】 本文讨论严格凸守恒律的初边值问题，其弱熵解在一类含有有限个间断的分片光滑函数中。由相应的初始值问题弱熵解的结构和Bardos-Leroux-Nedelec提出的边界熵条件，给出初边值问题弱熵解的一个构造方法。与初始值问题相比较，初边值问题的弱熵解包含了以下新的相互作用类型：中心稀疏波与边界相撞，边界反射出一个与之相切的新激波。根据弱熵解的结构和一些整体误差估计，使用匹配行波解方法证明了在L¹-范数下初边值问题的粘性逼近方法的整体误差估计。如果无粘解包含中心稀疏波与边界相撞且边界反射一个与之相切的新激波这样的相互作用，或者无粘解包含与边界相切的激波，那么在L¹-范数下粘性解与无粘解间的误差界是O(ε^1/2+ε|lnε|+ε)；否则，类似于初始值问题，误差界是O（ε|lnε|+ε）。更多还原

【Abstract】 This thesis is concerned with an initial-boundary value problem for strictly convex conservation laws whose weak entropy solution is in the piecewise smooth solution class consisting of finitely many discontinuities. By the structure of weak entropy solution of corresponding initial value problem and the boundary entropy condition which was developed by Bardos-Leroux-Nedelec, we give a construction method to the weak entropy solution of the initial-boundary value problem. Compared with the initial value problem, the weak entropy solution of the initial-boundary value problem includes the following new interaction type: a central rarefaction wave collides with the boundary and the boundary reflects a new shock wave which is tangent to the boundary. According to the structure and some global estimates of the weak entropy solution, we derive the global L1-error estimate for viscosity methods to this initial-boundary value problem by using the matching traveling wave solutions method. If the inviscid solution includes the interaction that a central rarefaction wave collides with the boundary and the boundary reflects a new shock wave which is tangent to the boundary, or the inviscid solution includes some shock wave which is tangent to the boundary, then the error of the viscosity solution to the inviscid solution isbounded by O in L1-norm; otherwise, as in the initial value problem, the error bound is O.更多还原