UNIFORM ATTRACTOR FOR WAVE EQUATION WITH NON-LINEAR DAMPING DEPENDING EXPLICITLY ON TIME

Abstract

The paper deals with long-time behavior of the solutions to the initial-boundary value problem for a non-autonomous non-linear wave equation. The peculiarity of the equation is the non-linear damping term depending explicitly on time. The problem is studied in the framework of the theory of processes and their attractors. The family of processes generated by the initial-boundary value problem is introduced. It is proved that this family is uniformly (with respect to the time-dependent damping coefficient) dissipative and asymptotically compact, thus possesses a unique uniform attractor. The attractor is a compact set in the common phase space of the processes.

Authors and Affiliations

O. O. NABOKA

Keywords

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  • EP ID EP398314
  • DOI -
  • Views 108
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How To Cite

O. O. NABOKA (2018). UNIFORM ATTRACTOR FOR WAVE EQUATION WITH NON-LINEAR DAMPING DEPENDING EXPLICITLY ON TIME. Вісник Національного технічного університету «ХПІ» Серія: Математичне моделювання в техніці та технологіях, 1(1279), 73-80. https://europub.co.uk/articles/-A-398314