| Global smooth solution of multi-dimensional non-homogeneous conservation laws |
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| 引用本文： | YANG Xiaozhou,ZHANG Tong. Global smooth solution of multi-dimensional non-homogeneous conservation laws[J]. 自然科学进展(英文版), 2004, 14(10): 855-862. DOI: 10.1080/10020070412331344451 |
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| 作者姓名： | YANG Xiaozhou ZHANG Tong |
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| 作者单位： | Department of Mathematics, Shantou University, Shantou 515063, China,Institute of Mathematics, Chinese Academy of Sciences, Beijing 100080, China |
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| 基金项目： | 国家自然科学基金，The Program of Key Laboratory of Military Defenses，教育部霍英东教育基金，教育部留学回国人员科研启动基金，广东省自然科学基金，中国奖学金委员会资助项目 |
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| 摘 要： | The initial value problem of multi-dimensional non-homogeneous conservation laws is studied and a sufficient condition of the existence of its global smooth solution is obtained. Additionally, three equivalent propositions of the existence of global smooth solution for multi-dimensional homogeneous scalar conservation laws are also obtained. The global smooth solution is uniquely expressed by the global implicit function that is determined by a scalar equation, not by a system as usual methods do.
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| 关 键 词： | conservation laws global smooth solution global implicit function diffeomorphism |
Global smooth solution of multi-dimensional non-homogeneous conservation laws |
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| Yang Xiaozhou,ZHANG Tong. Global smooth solution of multi-dimensional non-homogeneous conservation laws[J]. Progress in Natural Science, 2004, 14(10): 855-862. DOI: 10.1080/10020070412331344451 |
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| Authors: | Yang Xiaozhou ZHANG Tong |
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| Affiliation: | 1. Department of Mathematics, Shantou University, Shantou 515063, China
2. Institute of Mathematics, Chinese Academy of Sciences, Beijing 100080, China |
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| Abstract: | The initial value problem of multi-dimensional non-homogeneous conservation laws is studied and a sufficient condition of the existence of its global smooth solution is obtained. Additionally, three equivalent propositions of the existence of global smooth solution for multi-dimensional homogeneous scalar conservation laws are also obtained. The global smooth solution is uniquely expressed by the global implicit function that is determined by a scalar equation, not by a system as usual methods do. |
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| Keywords: | conservation laws global smooth solution global implicit function diffeomorphism |
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