The inverse Cauchy problem for a parabolic equation (Q2716187)
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scientific article; zbMATH DE number 1602254
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The inverse Cauchy problem for a parabolic equation |
scientific article; zbMATH DE number 1602254 |
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6 June 2001
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right hand side
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parabolic equation
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local existence and uniqueness
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0.96090263
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0.9601547
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0.9563599
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0.9542296
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0.9542296
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0.95139927
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The inverse Cauchy problem for a parabolic equation (English)
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Considered is the inverse problem of determining the right hand side \( f(t)g(x)\) of the following parabolic equation NEWLINE\[NEWLINE u_{t}(x,t) - a(t)u_{xx}(x,t)= f(t)g(x), NEWLINE\]NEWLINE where \(x\) in \(\mathbb{R}\), \(0<t<T\), and functions \( a(t)>0, u_{0}(x)=u(x,0), u_{1}(x)=u(x,T), \beta(t)=u(0,t)\) are given. Under the assumption that the Fourier transform of function \(u(x,t)\) is real with compact support, the author proves a theorem on local existence and uniqueness of the solution to the inverse problem.NEWLINENEWLINEFor the entire collection see [Zbl 0959.00006].
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