关于非主型偏微分方程的唯一性的一点注记 |
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引用本文: | 王光寅,麦明澂,陆柱家. 关于非主型偏微分方程的唯一性的一点注记[J]. 数学学报, 1979, 22(6): 713-718. DOI: cnki:ISSN:0583-1431.0.1979-06-005 |
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作者姓名: | 王光寅 麦明澂 陆柱家 |
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作者单位: | 中国科学院数学研究所(王光寅,麦明澂),中国科学院数学研究所(陆柱家) |
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摘 要: | <正> 1.引言 关于主型偏微分方程的Cauchy问题的唯一性的研究,已经十分充分.事实上,经典的Cauchy-Kovalevsky定理断言,解析方程的非特征Cauchy问题具有唯一性;而Goursat定理则断言,特征Cauchy问题的解必是唯一的,如果特征支柱上只具有单特征的话(参看Hormander[1]第五章).但是,对非主型方程,情形就大不相同.1974年,Treves研
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收稿时间: | 1977-10-13 |
修稿时间: | 1979-03-27 |
A REMARK ABOUT UNIQUENESS FOR THE PARTIAL DIFFERENTIAL EQUATIONS OF NON-PRINCIPAL TYPE |
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Affiliation: | Wang Guangyin Mai Mingcheng Lu Zhujia(Institute of Mathematics, Academia Sinica) |
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Abstract: | The partial differential equations of non-principal type are far from being wellunderstood. In 1974, F. Treves studied the following Cauchy problem where λ represents a real parameter. By. using the concatenation method, a diserete phenomenon is disclosed. For almost all values of λ, there is uniqueness. However, non-uniqueness occurs only for λ=1, 3, 5,… In this paper, by using energy integral method, we deal with the general second order PDE's of non-principal type in two variables and prove that non-uniqueness is a rare event. |
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