Seminar: Function spaces for variational solutions to parabolic-elliptic problems with moving interfaces

Thời gian: 10:00 đến 11:00 Ngày 05/03/2026

Địa điểm: Phòng C102, VIASM

Báo cáo viên: Lê Văn Chiến (Ghent University)

Tóm tắt: In this talk, I will present the key ingredients required to formulate the variational formulation for initial boundary-value problems of parabolic-elliptic PDEs posed on a fixed spatial domain containing time-dependent subdomains. The main difficulty arises from a coefficient in front of the time derivative that vanishes in part of the domain and is discontinuous across the moving interface. A class of function spaces that extend standard Sobolev–Bochner spaces will be introduced to capture this degeneracy and interface behavior. I will establish the density of smooth functions in these spaces, develop the corresponding “embedding” result, and derive an appropriate integration-by-parts formula. These results provide the foundation for the variational analysis of such coupled parabolic-elliptic systems.