Випадковий атрактор напівлінійного стохастичного збуреного хвильового рівняння без одиничності розв’язку
In this paper we investigate the dynamics of solutions of the semilinear wave equation, perturbed by additive white noise, in sense of the random attractor theory. The conditions on the parameters of the problem do not guarantee uniqueness of solution of the corresponding Cauchy problem. We prove th...
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| Date: | 2013 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | English |
| Published: |
The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute"
2013
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| Online Access: | http://journal.iasa.kpi.ua/article/view/57547 |
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| Journal Title: | System research and information technologies |
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System research and information technologies| Summary: | In this paper we investigate the dynamics of solutions of the semilinear wave equation, perturbed by additive white noise, in sense of the random attractor theory. The conditions on the parameters of the problem do not guarantee uniqueness of solution of the corresponding Cauchy problem. We prove theorem on the existence of random attractor for abstract noncompact multi-valued random dynamical system, which is applied to the wave equation with non-smooth nonlinear term. A priory estimate for weak solution of randomly perturbed problem is deduced, which allows to obtain the existence at least one weak solution. The multi-valued stochastic flow is generated by the weak solutions of investigated problem. We prove the existence of random attractor for generated multi-valued stochastic flow. |
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