Solvability of some many-dimensional versions of the Goursat problem for a first-order hyperbolic problem (Q2703942)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Solvability of some many-dimensional versions of the Goursat problem for a first-order hyperbolic problem |
scientific article |
Statements
4 February 2002
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characteristic problems
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Fourier transform
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classical and strong solutions
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integral representation
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Solvability of some many-dimensional versions of the Goursat problem for a first-order hyperbolic problem (English)
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The author studies the first-order hyperbolic system \(E_0U_t+AU_x+BU_y=F\), where NEWLINE\[NEWLINEE_0={1\;0\choose 0\;1},\quad A=\left(\begin{matrix} 1 & 0\\ 0 & -1\end{matrix}\right),\quad B=\left(\begin{matrix} 0 & -1\\ -1 & 0\end{matrix}\right),NEWLINE\]NEWLINE some characteristic problems (boundary value problems), that are multidimensional modifications of the Goursat problem.NEWLINENEWLINENEWLINEUsing the Fourier transform, he proves the existence and uniqueness of the classical and strong solutions. Also an integral representation of the regular solutions is given.
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