具有边界条件的双曲守恒律松弛逼近解的L^1收敛率  

L^1-convergence rate of relaxation approximations to conservation laws with boundary

作　　者：李晓萌[1] 崔慧萍[2] 刘红霞[1] 

机构地区：[1]暨南大学数学系,广东广州510632 [2]广东药学院基础学院数学教研室,广东广州510006

出　　处：《暨南大学学报（自然科学与医学版）》2009年第1期61-67,共7页Journal of Jinan University(Natural Science & Medicine Edition)

基　　金：国家自然科学基金资助项目(10571075);广东省自然科学基金资助项目(04010473)

摘　　要：讨论刚性松弛方程组初边值问题的松弛逼近解L1-收敛到其平衡态解的收敛率.在边界值为一个非超音速状态,初始值在此非超音速状态的小扰动的条件下,当平衡态解为具有有限条间断的分片光滑函数时,使用匹配行波解的方法导出松弛方程组的初边值问题的松弛解L1-收敛到其平衡态解的误差界为O(εlnε+ε).L^1-convergence rate of solutions to a stiff relaxation system with initial-boundary value condition to its equilibrium solutions is studied. Assume that the boundary data is a nontransonic state and initial data is a small perturbation, by using matching method and the traveling wave solutions, the error between the relaxation approximations and its equilibrium solution is estimated to be bounded by O（ε｜lnε｜＋ε） in L^1-norm, if the equilibrium solutions are piecewise smooth with finitely many discontinui- ties for the initial-boundary value problem of the stiff relaxation system.

关 键 词：初边值问题 守恒律 松弛逼近解 平衡态解 收敛率 

分 类 号：O174.52[理学—数学]