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Mathematics > Analysis of PDEs
Title: Inertial evolution of non-linear viscoelastic solids in the face of (self-)collision
(Submitted on 1 Dec 2022 (v1), last revised 1 Dec 2023 (this version, v2))
Abstract: We study the time evolution of non-linear viscoelastic solids in the presence of inertia and (self-)contact. For this problem we prove the existence of weak solutions for arbitrary times and initial data, thereby solving an open problem in the field. Our construction directly includes the physically correct, measure-valued contact forces and thus obeys conservation of momentum and an energy balance. In particular, we prove an independently useful compactness result for contact forces.
Submission history
From: Malte Kampschulte [view email][v1] Thu, 1 Dec 2022 18:08:45 GMT (42kb)
[v2] Fri, 1 Dec 2023 08:47:36 GMT (63kb)
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