| 水汽方程古典解的适定性研究 |
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| 引用本文： | 王必正.水汽方程古典解的适定性研究[J].气候与环境研究,2000,5(2):145-154. |
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| 作者姓名： | 王必正 |
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| 基金项目： | “国家重点基础研究发展规划”G1998040900项目第一部分和国家自然科学基金资助项目49805005和49735160 |
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| 摘 要： | 对于球坐标系下的水汽方程，当考虑水汽的凝结或凝华过程时，利用水汽方程的特点得到了关于水汽方程的弱极值原理的较强形式。利用该弱极大值原理，证明了对于第一类、第二类和第三类边值问题，水汽方程解的唯一性和稳定性。利用Schauder方法，证明了对于第一类、第二类和第三类边值问题，C2空间连续的水汽方程解的存在性。此外，还严格证明了水汽方程古典解的非负性。
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| 关 键 词： | 唯一性 稳定性 存在性 非负解 |
| 修稿时间： | 1999年3月22日 |
The Well-Posed Problems of The Classic Solution of Water Vapour Equation |
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| Wang Bizheng.The Well-Posed Problems of The Classic Solution of Water Vapour Equation[J].Climatic and Environmental Research,2000,5(2):145-154. |
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| Authors: | Wang Bizheng |
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| Abstract: | The well-posed problems of water vapour equation with condensation process were studied. By using the weak maximum principle, the uniqueness and stability of the solution of water vapour equation with the first, second and third boundary-value problems were proven. By using Schauder's method, the existence of class C 2solution of water vapour equation with the first, second and third boundary-value problems were proven. At last, it was proven that the classic solution of water vapour equation is non-negative. |
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| Keywords: | uniqueness stability existence non-negative solution |
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