| 二阶抛物型方程柯西反问题中系数的辨识 |
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| 引用本文： | 梁树培,石靖华.二阶抛物型方程柯西反问题中系数的辨识[J].湖北大学学报(自然科学版),1995,17(3):273-277. |
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| 作者姓名： | 梁树培 石靖华 |
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| 作者单位： | 武汉水利电力大学，湖北大学 |
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| 摘 要： | 对于形如ｕｔ（ｘ，ｔ）－（Ｌｕ）（ｘ，ｔ）＝ｑ（ｔ）ｕ（ｘ，ｔ）＋ｆ（ｘ，ｔ），ｕ（ｘ，ｏ）＝ψ（ｘ），ｕ（ｘ０，ｔ）＝ｈ（ｔ）的ｎ维二阶抛物型方程柯西反问题，利用柯西问题解的表达式及伏特拉积分方程，在经典意义下，得到示知函数ｕ（ｘ，ｔ）及其系数ｑ（ｔ）存在且唯一的结果。
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| 关 键 词： | 抛物型方程 解 初值问题 柯西反问题 |
IDENTIFICATION FOR A COEFFICIENT IN THE CAUCHY INVERSE PROBLEM OF THE 2-ORDER PARABOLIC EQUATION |
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| Liang Shupei,Shi Jinghua.IDENTIFICATION FOR A COEFFICIENT IN THE CAUCHY INVERSE PROBLEM OF THE 2-ORDER PARABOLIC EQUATION[J].Journal of Hubei University(Natural Science Edition),1995,17(3):273-277. |
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| Authors: | Liang Shupei Shi Jinghua |
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| Institution: | Liang Shupei;Shi Jinghua(Wuhan University of hydraulic and electric engineering)(Hubei University) |
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| Abstract: | For the inrerse cauchy problem of the n -dimension 2-order parabolic equation, its forme is ut(x,t)-(Lu )(x,t) =q(t)u(x,t)+f(x,t), u (x, 0) =(x),used the solution formula of the cauchy problem and volterra integral equation,the unknown fonction u(x,t)and its coefficient q(t) exist and are unique in the classical sence, we are obtained. |
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| Keywords: | Solution of the cauchy problem of the n-dimension 2-order parabolic equation Volterra integral equation |
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