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Elizabeth Its

2012-06-26
11:00:00 - 12:00:00

103 , Mathematics Research Center Building (ori. New Math. Bldg.)

The Riemann-Hilbert method was originated in the theory of integrable nonlinear PDEs. In the 90s, the method was extended to a number of new areas, and since then it has played an important role in solving a number of long- standing problems of analysis and mathematical physics. In the talk, we will present some recent developments in the Riemann-Hilbert approach obtained back in the PDE theory. This time, the Riemann-Hilbert techniques is applied to linear problems but in the domains which do not allow a direct separation of variables. We will focus on the solution of the boundary value problem for the Helmholtz equation in the quarter plane as a case study. If time permits, we shall also discuss the elastodynamic equation in the quarter plane.