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| 拟线性双曲-抛物奇异摄动问题的O(ε~2)阶渐近展开 | |
| 引用本文： | 陈国玉,沈锦仁. 拟线性双曲-抛物奇异摄动问题的O(ε~2)阶渐近展开[J]. 解放军理工大学学报(自然科学版), 2004, 0(6) |
| 作者姓名： | 陈国玉 沈锦仁 |
| 作者单位： | 解放军合肥炮兵学院 安徽合肥230001(陈国玉)，解放军理工大学理学院 江苏南京211101(沈锦仁) |
| 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。 |
| 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 |
Asymptotic Expansion for Quasi-liner Singular Perturbation Problem of Hyperbolic-parabolic Patial Differential Equation |
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| CHEN Guo-yu,SHEN Jin-ren. Asymptotic Expansion for Quasi-liner Singular Perturbation Problem of Hyperbolic-parabolic Patial Differential Equation[J]. Journal of PLA University of Science and Technology(Natural Science Edition), 2004, 0(6) | |
| Authors: | CHEN Guo-yu SHEN Jin-ren |
| Affiliation: | CHEN Guo-yu~1,SHEN Jin-ren~2 |
| Abstract: | 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. |
| Keywords: | quasi-liner singular perturbation problem hyperbolic-parabolic partial differential equation continuous stability inequality small parameter |
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