Inertial (self-)collisions of viscoelastic solids with Lipschitz boundaries
-
Antonín Češík
,
Giovanni Gravina
and
Malte Kampschulte
Abstract
We continue our study, started in [A. Češík, G. Gravina and M. Kampschulte, Inertial evolution of non-linear viscoelastic solids in the face of (self-)collision, Calc. Var. Partial Differential Equations 63 2024, 2, Paper No. 55], of (self-)collisions of viscoelastic solids in an inertial regime. We show existence of weak solutions with a corresponding contact force measure in the case of solids with only Lipschitz-regular boundaries. This necessitates a careful study of different concepts of tangent and normal cones and the role these play both in the proofs and in the formulation of the problem itself. Consistent with our previous approach, we study contact without resorting to penalization, i.e., by only relying on a strict non-interpenetration condition. Additionally, we improve the strategies of our previous proof, eliminating the need for regularization terms across all levels of approximation.
Funding source: Ministerstvo Školství, Mládeže a Tělovýchovy
Award Identifier / Grant number: LL2105
Funding source: Grantová Agentura České Republiky
Award Identifier / Grant number: 23-04766S
Funding source: Grantová Agentura, Univerzita Karlova
Award Identifier / Grant number: GA UK No. 393421
Funding source: Univerzita Karlova v Praze
Award Identifier / Grant number: UNCE/24/SCI/005
Funding statement: Antonín Češík and Malte Kampschulte acknowledge the support of the ERC-CZ grant LL2105 by the Czech Ministry of Education, Youth and Sports, and the support of Czech Science Foundation (GAČR) under grant No. 23-04766S. Antonín Češík further acknowledges the support of Charles University, project GA UK No. 393421, and Charles University Research Centre program No. UNCE/24/SCI/005.
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© 2024 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Boundary behavior of solutions to fractional p-Laplacian equation
- Existence of distributional solutions to some quasilinear degenerate elliptic systems with low integrability of the datum
- A weakly coupled system of p-Laplace type in a heat conduction problem
- On the interior regularity criteria for the viscoelastic fluid system with damping
- On the L 1-relaxed area of graphs of BV piecewise constant maps taking three values
- On prescribing the number of singular points in a Cosserat-elastic solid
- Stability from rigidity via umbilicity
- Free boundary regularity in the fully nonlinear parabolic thin obstacle problem
- Calderón–Zygmund theory for strongly coupled linear system of nonlocal equations with Hölder-regular coefficient
- Inertial (self-)collisions of viscoelastic solids with Lipschitz boundaries
- A discrete crystal model in three dimensions: The line-tension limit for dislocations
- Two-dimensional graph model for epitaxial crystal growth with adatoms
- Global existence for the Willmore flow with boundary via Simon’s Li–Yau inequality
- Linearization in magnetoelasticity
- The fractional Hopf differential and a weak formulation of stationarity for the half Dirichlet energy
Articles in the same Issue
- Frontmatter
- Boundary behavior of solutions to fractional p-Laplacian equation
- Existence of distributional solutions to some quasilinear degenerate elliptic systems with low integrability of the datum
- A weakly coupled system of p-Laplace type in a heat conduction problem
- On the interior regularity criteria for the viscoelastic fluid system with damping
- On the L 1-relaxed area of graphs of BV piecewise constant maps taking three values
- On prescribing the number of singular points in a Cosserat-elastic solid
- Stability from rigidity via umbilicity
- Free boundary regularity in the fully nonlinear parabolic thin obstacle problem
- Calderón–Zygmund theory for strongly coupled linear system of nonlocal equations with Hölder-regular coefficient
- Inertial (self-)collisions of viscoelastic solids with Lipschitz boundaries
- A discrete crystal model in three dimensions: The line-tension limit for dislocations
- Two-dimensional graph model for epitaxial crystal growth with adatoms
- Global existence for the Willmore flow with boundary via Simon’s Li–Yau inequality
- Linearization in magnetoelasticity
- The fractional Hopf differential and a weak formulation of stationarity for the half Dirichlet energy
