This paper has been withdrawn by Thierno Mamadou Balde

No PDF available, click to view other formats

Abstract:The framework of this article is cell motility modeling. Approximating cells as rigid spheres we take into account for both non-penetration and adhesions forces. Adhesions are modeled as a memory-like microscopic elastic forces. This leads to a delayed and constrained vector valued system of equations. We prove that the solution of these equations converges when {\epsilon}, the linkages turnover parameter, tends to zero to the a constrained model with friction. We discretize the problem and penalize the constraints to get an uncon?strained minimization problem. The well-posedness of the constrained problem is obtained by letting the penalty parameter to tend to zero. Energy estimates `a la De Giorgi are derived accounting for delay. Thanks to these estimates and the convexity of the constraints, we obtain compactness uniformly with respect to the discretisation step and {\epsilon}, this is the mathematically involved part of the article. Considering that the characteristic bonds lifetime goes to zero, we recover a friction model comparable to [Venel et al, ESAIM, 2011] but under more realistic assumptions on the external load, this part being also one of the challenging aspects of the work

Submission history

From: Thierno Mamadou Balde [view email]
[v1] Tue, 24 Dec 2024 17:12:01 UTC (141 KB)
[v2] Thu, 14 Aug 2025 14:57:43 UTC (1 KB) (withdrawn)
[v3] Tue, 23 Jun 2026 15:27:49 UTC (1 KB) (withdrawn)