Colloquium / Seminars
Topic：On strong convergence of an elliptic regularization with the Neumann boundary condition applied to a boundary value problem of a stationary advection equation
Speaker：Prof. Daiuske Kawagoe
Date time：Sep. 20, 2022 14:00 - 15:00
Abstract：Abstract. We consider a boundary value problem of a stationary advection equation with the homogeneous inflow boundary condition in a bounded domain with Lipschitz boundary, and consider its perturbation with respect to the Laplacian with a small positive parameter $\epsilon$. In this talk we show $L^2$ strong convergence of the perturbed solutions to the original solution in the domain and on a part of the boundary as the parameter $\epsilon$ tends to 0, and discuss its convergence rates assuming that the original solution has $H^1$ or $H^2$ regularity. A key observation is that the convergence rate depends not only on the regularity of the original solution but also on a relation between the boundary and the advection vector field. This talk is based on a joint work with Masaki Imagawa.