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IMA Journal of Applied Mathematics Advance Access published online on March 28, 2008
IMA Journal of Applied Mathematics, doi:10.1093/imamat/hxn008
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© The Author 2008. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Dynamics of electrorheological clutch and a problem for non-linear parabolic equation with non-local boundary conditions

W. G. Litvinov{dagger}

Institute of Mathematics, University of Augsburg, Universitätsstrasse 14, D-86159 Augsburg, Germany

{dagger} Email: litvinov{at}math.uni-augsburg.de

Received on May 18, 2007; Accepted on August 30, 2007

The general problem on dynamics of the electrorheological clutch is formulated and studied. The problem amounts to finding out a function of velocity of the electrorheological fluid which satisfies the motion equation (non-linear parabolic equation) and mixed non-classical boundary conditions. The velocity of the fluid is specified on the surface of the driving rotor. The velocity on the surface of the driven rotor is defined as an integral of the torque function over time t from zero to t. The torque function is computed upon integrating the shear stresses (non-linear functions of derivatives of the velocity) over the surface of the driven rotor. Approximate problem is formulated in a form of a problem with a delay. It is proved the existence and the uniqueness of the solution of the initial and approximate problems and the convergence of the solutions of the approximate problem to the solution of the initial problem as the parameter of delay tends to zero.

Keywords: electrorheological fluid; rotor; torque; delay; existence; smooth solution.


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