Global existence for a nonlocal model for adhesive contact. Issue 8 (11th June 2018)

• Record Type: Journal Article
• Authors: Bonetti, Elena; Bonfanti, Giovanna; Rossi, Riccarda
• Is Part Of: Applicable analysis. Volume 97:Issue 8(2018)
• Page Start: 1315
• Page End: 1339
• Publication Date: 2018-06-11
• Subjects: Contact -- adhesion -- nonlocal damage -- existence results; 35K55 -- 35Q72 -- 74A15 -- 74M15; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2017.1359567
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract: In this paper, we address the analytical investigation into a model for adhesive contact introduced in a paper by Freddi and Fremond, which includes nonlocal sources of damage on the contact surface, such as the elongation. The resulting PDE system features various nonlinearities rendering the unilateral contact conditions, the physical constraints on the internal variables, as well as the contributions related to the nonlocal forces. For the associated initial-boundary value problem, we obtain a global-in-time existence result by proving the existence of a local solution via a suitable approximation procedure and then by extending the local solution to a global one by a nonstandard prolongation argument.