Nonlocal conservation laws on bounded domains.

par Dr Ola Mæhlen (University of Oslo)

jeudi 9 mars 2023, 14:00 → 16:00 Europe/Paris

E2290 (Tours)

We provide an entropy-formulation of parabolic equations, posed on bounded domains, that feature nonlocal degenerate diffusion. The nonlocal diffusions considered are those represented by symmetric Lévy operators (including all fractional Laplacians). These operators are not well defined when applied to functions on bounded domains, which we tackle by posing Dirichlet ‘boundary conditions’ in the full complement of our domain of interest.

I will give an overview of the arguments for the existence and uniqueness of corresponding entropy solutions and explain how these arguments differ from the local case. Some theory on Lévy operators will also be discussed.

This is joint work with

• Espen R. Jakobsen (Norwegian University of Science and Technology),
• Jørgen Endal (Norwegian University of Science and Technology) and  
• Nathaël Alibaud (Université de Bourgogne Franche-Comté)