一类高阶超双曲型方程的中量定理及其逆定理

同小军; 同登科; 陈绵云

一类高阶超双曲型方程的中量定理及其逆定理

1.
华中理工大学自控系, 武汉430074;
2.
石油大学应用数学系, 山东东营257062

基金项目: 国家自然科学基金资助项目(79970025)

详细信息

作者简介:
同小军(1967- ),男,陕西富平人,讲师,硕士,研究方向为偏微分方程及模糊控制的理论及应用.

中图分类号: O175.27
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- 被引次数: 0
出版历程
- 收稿日期: 1999-10-29
- 修回日期: 2001-01-28
- 刊出日期: 2001-06-15

The Mean Value Theorem and Converse Theorem of One Class the Fourth Order Partial Differential Equations

1.
Department of Automation Control, Huazhong University of Science and Technology, Wuhan 430074, P R China;
2.
Department of Applied Mathematics, University of Petroleum, Dongying, Shando 257062, P R China

摘要

摘要: Asgeirsson中量定理表明超双曲型方程的Cauchy问题一般是不适定的,对Asgeirsson中量定理的推广就有重要意义。目前关于高阶方程解的中量只有初步探讨,尚未得到具体结果,本文直接利用Asgeirsson中量定理结果和积分、微分的性质与关系,得到了高阶方程解的中量满足广义双轴对称位势方程,同时还证明了其逆定理。利用关于广义双轴对称位势方程正则解的表达式及雅可比多项式的特殊性质,得到了高阶方程解的中量公式,从而使得关于解的拓展性和适定性的讨论将有可能。
- Asgirsson中量定理 /
- 广义双轴对称位势方程 /
- 雅可比多项式
Abstract: For the formal presentation about the definite problems of ultra-hyperbolic equations,the famous Asgeirsson mean value theorem has answered that Cauchy problems are ill-posed for ultra-hyperbolic partial differential equations of the second order.So it is important to develop Asgeirsson mean value theorem.The mean value of solution for the higher order equation has been discussed primarily and has no exact result at present.The mean value theorem for the higher order equation can be deduced and satisfied generalized biaxial symmetry potential equation by using the result of Asgeirsson mean value Theorem and the properties of derivation and integration.Moreover,the mean value formula can be obtained by using the regular solutions of potential equation and the special properties of Jacobi polynomials.Its converse theorem is also proved.The obtained results make it possible to discuss on continuation of the solutions and well posed problem.
- Asgeirsson mean value theorem /
- generalized biaxial symmetry potential equation /
- Jacobi polynomials

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参考文献(6)

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