Publication: On the asymptotic behavior of solutions of a damped oscillator under a sublinear friction term
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2001
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Liñán Martínez, Amable
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Real Academia Ciencias Exactas Físicas Y Naturales
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Abstract
We show that there are two curves of initial data (xo, vo) for which the solutions x(t) of the corresponding Cauchy problem associated to the equation xtt + |xí|a_1 xt + x — 0, where a G (0,1), vanish after a finite time. By using asymptotic and methods and comparison arguments we show that for many other initial data the solutions decay to 0, in an infinite time, as i-"/í1-").
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Comunicación Preliminar / Preliminary Communication
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Brezis, H. (1972). Opérateurs maximaux monotones et semigroupes de contractions dans les espaces de Hilbert, North-Holland, Amsterdam.
Díaz, J. I. and Liñán, A. (2002). On the asymptotic behavior of solutions of a damped oscillator under a sublinear friction term: from the exceptional to the generic behaviors. To appear in Advences in PDE, Lecture Notes in Pure and Applied Mathematics (A. Benkirane and A. Touzani. eds.), Marcel Dekker.
Díaz, J. I. and Liñán, A.,On the dynamics of a constrained oscillator as limit of oscillators under an increasing superlinear friction. To appear.
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Jordan, D. W. and Smith, P. (1979). Nonlinear Ordinary Differential Equations, (Second Edition), Clarendon Press, Oxford.
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