On necessary conditions for the Cauchy problem for evolution equations to be well posed in the class \(C^ \infty\) (Q1210065)
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scientific article; zbMATH DE number 169028
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On necessary conditions for the Cauchy problem for evolution equations to be well posed in the class \(C^ \infty\) |
scientific article; zbMATH DE number 169028 |
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On necessary conditions for the Cauchy problem for evolution equations to be well posed in the class \(C^ \infty\) (English)
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16 May 1993
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The author studies the Cauchy problem for equations of the form \[ Lu(t, x)= \Biggl[ t^k \partial^m_t- \sum^m_{j= 1} a_j(t, x_j \partial_x) \partial^{m- j}_t\Biggr] u(t, x)= 0,\;(t, x)\in [\tau, T]\times \Omega, \] with \(C^\infty\)-coefficients. He gives necessary conditions for this problem to have a unique solution.
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microlocal energy
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well-posedness
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