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We consider an inverse problem for the nonlinear Boltzmann equation with a time-dependent kernel in dimensions n \geq 2. We establish a logarithm-type stability result for the collision kernel from measurements under certain additional conditions. A uniqueness result is derived as an immediate consequence of the stability result. Our approach relies on second-order linearization and multivariate finite differences, as well as the stability of the light-ray transform.
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One-period stability analysis of polygonal sweeping processes with application to an elastoplastic model
We offer a finite-time stability result for Moreau sweeping processes on the plane with periodically moving polyhedron. The result is used to establish the convergence of stress evolution of a simple network of elastoplastic springs to a unique cyclic response in just one cycle of the external displacement-controlled cyclic loading. The paper concludes with an example showing that smoothing the vertices of the polyhedron makes finite-time stability impossible.
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- Award ID(s):
- 1916876
- PAR ID:
- 10151263
- Date Published:
- Journal Name:
- Mathematical Modelling of Natural Phenomena
- Volume:
- 15
- ISSN:
- 0973-5348
- Page Range / eLocation ID:
- 25
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1051/mmnp/2019030
