PDE Seminar

DATE2022-09-27 16:00-17:00

PLACE數學系館 3F會議室

SPEAKER川越大輔 助理教授(京都大學

TITLEOn Strong Convergence of an Elliptic Regularization with the Neumann Boundary Condition Applied to a Boundary Value Problem of a Stationary Advection Equation

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.