BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Antoine Zurek (Technische Universität Wien\, Austria) DTSTART:20210323T140000Z DTEND:20210323T150000Z DTSTAMP:20260423T024743Z UID:CRM-CAMP/44 DESCRIPTION:Title: Existence of traveling wave solutions for the Diffusion Poisson Coupled Model: a computer-assisted proof\nby Antoine Zurek (Technische Univers ität Wien\, Austria) as part of CRM CAMP (Computer-Assisted Mathematical Proofs) in Nonlinear Analysis\n\n\nAbstract\nIn France one option under st udy for the storage of high-level radioactive waste is based on an undergr ound repository. More precisely\, the waste shall be confined in a glass m atrix and then placed into cylindrical steel canisters. These containers s hall be placed into micro-tunnels in the highly impermeable Callovo-Oxford ian claystone layer at a depth of several hundred meters. The Diffusion Po isson Coupled Model (DPCM) aims to investigate the safety of such long ter m repository concept by describing the corrosion processes appearing at th e surface of carbon steel canisters in contact with a claystone formation. It involves drift-diffusion equations on the density of species (electron s\, ferric cations and oxygen vacancies)\, coupled with a Poisson equation on the electrostatic potential and with moving boundary equations. So far \, no theoretical results giving a precise description of the solutions\, or at least under which conditions the solutions may exist\, are avalaible in the literature. However\, a finite volume scheme has been developed to approximate the equations of the DPCM model. In particular\, it was obser ved numerically the existence of traveling wave solutions for the DPCM mod el. These solutions are defined by stationary profiles on a fixed size dom ain with interfaces moving at the same velocity. The main objective of thi s talk is to present how we apply a computer-assisted method in order to p rove the existence of such traveling wave solutions for the system. This a pproach allows us to obtain for the first time a precise and certified des cription of some solutions. \nThis work is in collaboration with Maxime Br eden and Claire Chainais-Hillairet.\n LOCATION:https://researchseminars.org/talk/CRM-CAMP/44/ END:VEVENT END:VCALENDAR