| STABILIZED NUMERICAL APPROXIMATIONS OF THE BACKWARD PROBLEM OF A PARABOLIC EQUATION |
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| 作者姓名： | 韩厚德 胡刚 |
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| 作者单位： | Han Houde Hu GangDepartment of Mathematical Sciences，Tsinghua University，Beijing 100084，PRC.Department of Applied Mathematics，California Institute of Technology，Paseadena，CA 91125，USA. |
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| 基金项目： | This work was supported partly by the Special Funds for Major State Basic Reseach Projects of China and the Na-tional Natural Science Foundation of China |
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| 摘 要： | 1 IntroductionLetΩ be a bounded domain in Rn and Ω be its boundary.ThenΣ =Ω× ( 0 ,1 ) is abounded domain in Rn+1 .We consider the following backwad problem of a prabolic equa-tion: u t= ni,j=1 xiaij( x) u xj -c( x) u, ( x,t)∈Σ,( 1 )u| Ω× 0 ,1 ] =0 , ( 2 )u| t=1 =g( x) . ( 3 ) Where { aij( x) } are smooth functions given onΩ satisfyingaij( x) =aji( x) , 1≤ i,j≤ n, ( 4)α0 ni=1ζ2i ≤ ni,j=1aij( x)ζiζj≤α1 ni=1ζ2i, ζ∈ Rn,x∈Ω. ( 5) Where0 <α…
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STABILIZED NUMERICAL APPROXIMATIONS OF THE BACKWARD PROBLEM OF A PARABOLIC EQUATION |
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| Han Houde,Hu Gang.STABILIZED NUMERICAL APPROXIMATIONS OF THE BACKWARD PROBLEM OF A PARABOLIC EQUATION[J].Numerical Mathematics A Journal of Chinese Universities English Series,2001,10(2). |
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| Authors: | Han Houde Hu Gang |
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| Institution: | 1. Department of Mathematical Sciences, Tsinghua University, Beijing 100084
2. Department of Applied Mathematics, California Institute of Technology,Paseadena, CA 91125, USA |
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| Abstract: | In this paper, the backward problem of a parabolic equation is considered. Three new stability estimates are given. Based on the new stability estimates, a regularization method is proposed for which error estimates are available. The regularization method can be used for the numerical approximations of the original problem which will be shown by the numerical examples. |
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| Keywords: | backward parabolic equation stability estimates regularization method |
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