| Title: |
Analysis of a one dimensional energy dissipating free boundary model with nonlinear boundary conditions. Existence of weak solutions |
| Authors: |
Merlet, Benoît; Venel, Juliette; Zurek, Antoine |
| Contributors: |
Laboratoire Paul Painlevé - UMR 8524 (LPP); Université de Lille-Centre National de la Recherche Scientifique (CNRS); Reliable numerical approximations of dissipative systems (RAPSODI); Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centre Inria de l'Université de Lille; Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria); Université Polytechnique Hauts-de-France (UPHF); Laboratoire de Mathématiques Appliquées de Compiègne (LMAC); Université de Technologie de Compiègne (UTC) |
| Source: |
https://hal.science/hal-03888607 ; 2025. |
| Publisher Information: |
CCSD |
| Publication Year: |
2025 |
| Collection: |
Université Polytechnique Hauts-de-France: HAL |
| Subject Terms: |
Corrosion model; moving boundary problem; existence analysis; minimizing scheme; [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] |
| Description: |
This work is part of a general study on the long-term safety of the geological repository of nuclear wastes. A diffusion equation with a moving free boundary in one dimension is introduced and studied. The model describes some mechanisms involved in corrosion processes at the surface of carbon steel canisters in contact with a claystone formation. The main objective of the paper is to prove the existence of weak solutions to the problem which are maximal in time. For this, a time semidiscrete minimizing movements scheme based on a Wasserstein-like distance is introduced. The existence of solutions to the scheme is proved. Then, using a priori estimates, it is shown that as the time step goes to zero these solutions converge up to extraction towards a maximal weak solution to the free boundary model. |
| Document Type: |
report |
| Language: |
English |
| Availability: |
https://hal.science/hal-03888607; https://hal.science/hal-03888607v2/document; https://hal.science/hal-03888607v2/file/MVZ_2025.pdf |
| Rights: |
info:eu-repo/semantics/OpenAccess |
| Accession Number: |
edsbas.6116EB8B |
| Database: |
BASE |