Smooth Solution of the Dirichlet Problem for a Quasilinear Hyperbolic Equation of the Second Order
On the basis of the exact solution of the linear Dirichlet problem \(u_{tt} - u_{xx} = f\left( {x,t} \right)\) , \(u\left( {0,t} \right) = u\left( {\pi ,t} \right) = 0,{\text{ }}u\left( {x,0} \right) = u\left( {x,2\pi } \right) = 0,\) \(0 \leqslant x \leqslant \pi ,{\text{ }}0 \leqslant t \...
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| Datum: | 2000 |
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| Hauptverfasser: | , , , , , |
| Format: | Artikel |
| Sprache: | Ukrainisch Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2000
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/4492 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | On the basis of the exact solution of the linear Dirichlet problem \(u_{tt} - u_{xx} = f\left( {x,t} \right)\) , \(u\left( {0,t} \right) = u\left( {\pi ,t} \right) = 0,{\text{ }}u\left( {x,0} \right) = u\left( {x,2\pi } \right) = 0,\) \(0 \leqslant x \leqslant \pi ,{\text{ }}0 \leqslant t \leqslant 2\pi ,\) we obtain conditions for the solvability of the corresponding Dirichlet problem for the quasilinear equation u tt − u xx = f(x, t, u, u t). |
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