扩散占优的2×2双曲平衡律奇异松弛极限及其应用  

Singular Limits of Stiff Relaxation and Dominant Diffusion for Hyperbolic Balance Laws and Its Applications

作　　者：宋国强[1,2] 杨瑞芳[1] 赵磊[1] 李丽娜[1] 

机构地区：[1]南京航空航天大学理学院,江苏南京210016 [2]安徽医科大学卫生管理学院,安徽合肥230032

出　　处：《吉林大学学报（理学版）》2009年第3期416-424,共9页Journal of Jilin University:Science Edition

基　　金：安徽省教育厅自然科学基金(批准号:2005KJ207);南京航空航天大学杰出人才基金(批准号:1008-904319)

摘　　要：研究一般扩散占优的2×2双曲平衡律系统奇异松弛极限,用补偿紧性方法,在松弛时间τ比扩散系数ε趋于零快时,即τ=o(ε),ε→0时,得到其解的整体存在性一般框架:如果上述系统的解存在对ε一致的先验L∞估计,则其解序列收敛于上述系统的对应平衡状态解.并将这一框架应用于一些具有非齐次项和松弛项的重要非线性系统,如有非齐次项和松弛项的二次流、LeRoux系统、非线性弹性系统和交通扩展流等.The authors investigated the singular limits of stiff relaxation and dominant diffusion for general 2×2 nonlinear systems of balance laws, that is, τ=0（ε）, ε→0, the relaxation time τ tends to zero faster than the diffusion parameter ε. If there exists a priori L∞ bound that is uniformly with respect to s for the solutions of a system, then the solution sequence converges to the corresponding equilibrium solution of the system. This framework can be applied to some important nonlinear systems with relaxation terms and inhomo-geneous terms, such as the system of quadratic flux, the LeRoux system, the system of elasticity and the extended models of traffic flows.

关 键 词：双曲平衡律 奇异松弛极限 非齐次项 弱解 补偿紧性方法 

分 类 号：O175.27[理学—数学]