拟线性双曲-抛物奇异摄动问题的O（ε2）阶渐近展开  

Asymptotic Expansion for Quasi-liner Singular Perturbation Problem of Hyperbolic-parabolic Patial Differential Equation

作　　者：陈国玉[1] 沈锦仁[2] 

机构地区：[1]解放军合肥炮兵学院,安徽合肥230001 [2]解放军理工大学理学院,江苏南京211101

出　　处：《解放军理工大学学报（自然科学版）》2004年第6期91-94,共4页Journal of PLA University of Science and Technology(Natural Science Edition)

摘　　要：为了讨论一个拟线性双曲-抛物奇异摄动的渐近展开问题,首先用能量方法建立稳定不等式,然后利用双重迭代法对原问题进行渐近展开,最后用稳定不等式证明了渐近解对原问题解的O(ε2)阶逼近式,从而证明了渐进解的一致有效性。A singular perturbation problem of a quasi-liner hyperbolic-parabolic partial differential equation is discussed. In order to discuss the asymptotic expansion of this problem, the energy method is applied to show the continuous stability inequality and the 2-order asymptotic expansion of the solution to this problem with respect to small parameter obtained. Thus the uniform effectiveness of the asymptotic expansion is proved.

关 键 词：拟线性双曲抛物奇异摄动问题 连续稳定不等式 小参数 

分 类 号：O175.1[理学—数学]