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Head-media interaction in magnetic recording. (English) Zbl 1009.34016

The authors study a boundary value problem for a coupled system of two nonautonomous ordinary differential equations representing a model for tape-head interaction in magnetic recording. A theorem for the existence of a smooth solution when the magnetic head has a discontinuous profile is proven. For clarity, the case of twice continuously differentiable profiles is first discussed by using a method of sub- and super-solutions and Schauder’s fixed-point theorem. Finally, the discussion is generalized to the discontinuous profile case.

MSC:

34B15 Nonlinear boundary value problems for ordinary differential equations
82D40 Statistical mechanics of magnetic materials
34A36 Discontinuous ordinary differential equations
34C60 Qualitative investigation and simulation of ordinary differential equation models
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References:

[1] Bhushan, B., Tribology and Mechanics of Magnetic Storage Devices (1990), Springer-Verlag: Springer-Verlag New York
[2] Bhushan, B., Mechanics and Reliability of Flexible Magnetic Media (1992), Springer-Verlag: Springer-Verlag New York
[3] Friedman, A., Mathematics in Industrial Problems. Mathematics in Industrial Problems, IMA, 67 (1994), Springer-Verlag: Springer-Verlag New York · Zbl 0848.00012
[4] Friedman, A.; Hu, B., Head-media interaction in magnetic recording, Arch. Rational Mech. Anal., 140, 79-101 (1997) · Zbl 0894.35114
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