| 一类二维分数阶偏微分方程解的适定性 |
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| 引用本文： | 苏延辉. 一类二维分数阶偏微分方程解的适定性[J]. 福州大学学报(自然科学版), 2015, 43(4): 435-439 |
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| 作者姓名： | 苏延辉 |
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| 作者单位： | 福州大学数计学院 |
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| 基金项目： | 福建省自然科学基金资助项目（面上项目，重点项目，重大项目）;国家自然科学基金项目（面上项目，重点项目，重大项目） |
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| 摘 要： | 研究一类二维分数阶偏微分方程的边值问题,主要包括两方面内容:一是研究了合适的分数阶Sobolev空间及分数阶算子的性质;二是发展了一个弱解的理论框架,并建立了弱解的适定性理论.这是构造数值方法(如有限元和谱方法等)求解二维分数阶偏微分方程的理论基础.
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| 关 键 词： | 分数阶导数；弱解；变分形式；适定性 |
| 修稿时间： | 2015-04-07 |
Well-posedness of the 2D-fractional partial differential equations |
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| SU Yanhui. Well-posedness of the 2D-fractional partial differential equations[J]. Journal of Fuzhou University(Natural Science Edition), 2015, 43(4): 435-439 |
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| Authors: | SU Yanhui |
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| Affiliation: | College of mathematics and computer science |
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| Abstract: | In this work, we investigate the boundary value problem of two-dimensional fractional partial differential equations (FEPDEs). The main contributions of this work are twofold: first, we investigate suitable fractional Sobolev spaces for fractional partial differential equations and study the properties of the fractional operator. Then, we develop a theoretical framework of weak solution and establish the well-posedness of the weak solution. Consequently, this work provides the theory for constructing numerical method such as finite element method and spectral method for solving the fractional partial differential equations. |
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| Keywords: | Fractional derivative weak solution variation formulation well-posedness |
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