| 一类偏微分方程的边值问题适定的充分必要条件 |
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| 引用本文： | 彭跃军.一类偏微分方程的边值问题适定的充分必要条件[J].同济大学学报(自然科学版),1988(1). |
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| 作者姓名： | 彭跃军 |
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| 作者单位： | 同济大学应用数学系 |
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| 摘 要： | 本文通过对平面带角点的区域中普通Sobolev空间H~1函数在角点附近边界性质的讨论,以及H~1与带权Sobolev空间H~(1.1)的联系,利用空间H~(1/2)的一个等价范数,给出了一系列函数集合非空的充分必要条件。利用这一结果,得到了在区域内部未知函数具有强间断的拟线性椭圆型偏微分方程的边值问题广义解存在唯一的充分必要条件。
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| 关 键 词： | 偏微分方程 广义解 变换 |
A Sufficient and Necessary Condition for the Boundary Value Problem of a Class of Partial Differential Equation Which is Well-Posed |
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| Peng Yuejun,.A Sufficient and Necessary Condition for the Boundary Value Problem of a Class of Partial Differential Equation Which is Well-Posed[J].Journal of Tongji University(Natural Science),1988(1). |
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| Authors: | Peng Yuejun |
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| Institution: | Department of Applied Mathematics |
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| Abstract: | In this paper, some boundary properties of Sobolev Space H~1 near the angularpoint are considered. Here we first discuss the relation between space H~1 andH~(1,1), then obtain the sufficient and necessary condition of a class of set which isnot empty by using equivalent norms of space H~(1/2). As an application, we studythe boundary value problem of quasi-harmonic partial differential equation withstrong discontinuity for the unknown variable in interface of domain and provethat the condition is also sufficient and necessary for this problem which is well.posed. |
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| Keywords: | Partial differential equation Generalized-solution Transformation |
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