Mixed problem for a nonlinear hyperbolic equation in a domain unbounded with respect to space variables
We investigate the first mixed problem for a quasilinear hyperbolic equation of the second order with power nonlinearity in a domain unbounded with respect to space variables. We consider the case of an arbitrary number of space variables. We obtain conditions for the existence and uniqueness of t...
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| Date: | 2007 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | Ukrainian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2007
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/3408 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | We investigate the first mixed problem for a quasilinear hyperbolic equation of the second order with power nonlinearity in a domain
unbounded with respect to space variables. We consider the case of an arbitrary number of space variables. We obtain conditions for the
existence and uniqueness of the solution of this problem independent of the behavior of solution as $|x| \rightarrow +\infty$.
The indicated classes of the existence and uniqueness are defined as spaces of local integrable functions. The dimension of the domain in no way limits the order of nonlinearity. |
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