| 一类具多项式系数偏微分方程的Cauchy问题 |
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| 引用本文： | 冯学尚.一类具多项式系数偏微分方程的Cauchy问题[J].兰州大学学报(自然科学版),1991,27(4):1-9. |
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| 作者姓名： | 冯学尚 |
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| 作者单位： | 兰州大学数学系 兰州，730000 |
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| 摘 要： |
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| 关 键 词： | 柯西问题 偏微分方程 多项式 系数 |
The Cauchy Problem for a Class of Linear Partial Differential Equations with Polynomial Coefficients |
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| Feng Xueshang.The Cauchy Problem for a Class of Linear Partial Differential Equations with Polynomial Coefficients[J].Journal of Lanzhou University(Natural Science),1991,27(4):1-9. |
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| Authors: | Feng Xueshang |
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| Institution: | Feng Xueshang Department of Mathematics,Lanzhou University,Lanzhou,730000 |
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| Abstract: | In this paper the existence, uniqueness and smoothness of solutionsto the Cauchy problem for a class of linear partial differential equationswith polynomial cofficients are discussed by using B. Simon's Hermiteexpressions about tempered distribution space. As simple applications,the fundamental solution to the Schrodinger equation u/t = iHu for thequantum mechanical harmonic oscillator and Mehler's famous formulafor the fundamental solution to u/t=-Hu are derived in this paper. |
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| Keywords: | tempered distribution space Hermite expressions Cauchy problem |
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