Mielke, A. and Rossi, R. and Savaré, G. (2016) BalancedViscosity solutions for multirate systems. Journal of Physics: Conference Series, 727 . pp. 127.

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Official URL: http://dx.doi.org/10.1088/17426596/727/1/012010
Abstract
Several mechanical systems are modeled by the static momentum balance for the displacement u coupled with a rateindependent flow rule for some internal variable z. We consider a class of abstract systems of ODEs which have the same structure, albeit in a finitedimensional setting, and regularize both the static equation and the rateindependent flow rule by adding viscous dissipation terms with coeficients \epsilon^\alpha and \epsilon, where 0 < \epsilon << 1 and \alpha > 0 is a fixed parameter. Therefore for \alpha\neq 1 u and z have different relaxation rates.<br /> We address the vanishingviscosity analysis as \epsilon\downarrow 0 of the viscous system. We prove that, up to a subsequence, (reparameterized) viscous solutions converge to a parameterized curve yielding a Balanced Viscosity solution to the original rateindependent system, and providing an accurate description of the system behavior at jumps. We also give a reformulation of the notion of Balanced Viscosity solution in terms of a system of subdifferential inclusions, showing that the viscosity in u and the one in z are involved in the jump dynamics in different ways, according to whether \alpha > 1, \alpha = 1, and \alpha\in (0, 1).
Item Type:  Article 

Subjects:  Mathematical and Computer Sciences > Mathematics > Numerical Analysis 
Divisions:  Department of Mathematics and Computer Science > Institute of Mathematics 
ID Code:  2152 
Deposited By:  Silvia Hoemke 
Deposited On:  07 Dec 2017 17:50 
Last Modified:  08 Dec 2017 14:21 
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