On an asymptotically autonomous system with Tikhonov type regularizing term |
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Authors: | Mohamed Ali Jendoubi Ramzi May |
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Institution: | 1. Institut Préparatoire aux Etudes Scientifiques et Techniques, Université 7 novembre à Carthage, B.P. 51, 2070, La Marsa, Tunisia 2. Département de Mathématiques, Faculté des sciences de Bizerte, Université 7 novembre à Carthage, 7021, Jarzouna, Tunisia
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Abstract: | We study the asymptotic behaviour of the trajectories of the second order equation ${\ddot{x}(t)+\gamma \dot{x}(t)+\nabla\phi(x(t))+\varepsilon(t)x(t)=g(t)}We study the asymptotic behaviour of the trajectories of the second order equation (x)\ddot](t)+g(x)\dot](t)+?f(x(t))+e(t)x(t)=g(t){\ddot{x}(t)+\gamma \dot{x}(t)+\nabla\phi(x(t))+\varepsilon(t)x(t)=g(t)} , where γ > 0, g ? L1(0,+¥;H){g \in L^1(0,+\infty;H)}, Φ is a C
2 convex function and e{\varepsilon} is a positive nonincreasing function. |
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Keywords: | |
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