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On the asymptotic behavior of solutions of a damped oscillator under a sublinear friction term

Díaz Díaz, Jesús Ildefonso and Liñán Martínez, Amable (2001) On the asymptotic behavior of solutions of a damped oscillator under a sublinear friction term. Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A: Matemáticas , 95 (1). pp. 155-160. ISSN 1578-7303

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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-").

Item Type:Article
Additional Information:Comunicación Preliminar / Preliminary Communication
Uncontrolled Keywords:sublinear damped oscillator, Coulomb friction, extinction in a finite time.
Subjects:Sciences > Mathematics > Differential equations
ID Code:15561
References:

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.

Haraux, A. (1979). Comportement à l'infini pour certains systèmes dissipatifs non linéaires, Proc. Roy. Soc. Edinburgh, 84A, 213-234.

Jordan, D. W. and Smith, P. (1979). Nonlinear Ordinary Differential Equations, (Second Edition), Clarendon Press, Oxford.

Kuo Pen-Yu and Vazquez, L. (1982). Numerical solution of an ordinary differential equation, Anales de Física, Serie B, 78, 270-272.

Deposited On:11 Jun 2012 07:48
Last Modified:06 Feb 2014 10:27

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