On a structured model for the load dependent reaction kinetics of transient elastic linkages mediating nonlinear friction

Milisic, Vuc and Oelz, Dietmar (2015) On a structured model for the load dependent reaction kinetics of transient elastic linkages mediating nonlinear friction. SIAM Journal on Mathematical Analysis, 47 3: 2104-2121. doi:10.1137/130947052


Author Milisic, Vuc
Oelz, Dietmar
Title On a structured model for the load dependent reaction kinetics of transient elastic linkages mediating nonlinear friction
Journal name SIAM Journal on Mathematical Analysis   Check publisher's open access policy
ISSN 0036-1410
1095-7154
Publication date 2015-01-01
Sub-type Article (original research)
DOI 10.1137/130947052
Open Access Status Not yet assessed
Volume 47
Issue 3
Start page 2104
End page 2121
Total pages 18
Place of publication Philadelphia, PA, United States
Publisher Society for Industrial and Applied Mathematics
Language eng
Formatted abstract
We consider a microscopic model for friction mediated by transient elastic linkages introduced in [D. Oelz and C. Schmeiser, Arch. Ration. Mech. Anal., 198 (2010), pp. 963-980; D. Oelz, C. Schmeiser, and V. Small, Cell Adh. Migr., 2 (2008), pp. 117-126]. In this study we extend results and the general approach employed in [V. Milisić and D. Oelz, J. Math. Pures Appl. (9), 96 (2011), pp. 484-501]. We introduce a new unknown and reformulate the model. Based on this framework, we derive new a priori estimates. In a first step this approach allows us to reproduce results of our earlier paper concerning the convergence of the system to a macroscopic friction law in the semicoupled case, but under weaker assumptions. Furthermore, we consider the fully coupled case and prove existence and uniqueness of the solution.
Keyword Friction coefficient
Protein linkages
Effect of chemical bonds
Cell adhesion
Renewal equation
Integro-differential equations
Volterra kernel
Fixed point
Nonlinear strain-stress
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Non-UQ

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Mathematics and Physics
 
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Created: Sat, 14 Jan 2017, 01:53:10 EST by Kay Mackie on behalf of School of Mathematics & Physics