Celebratio Mathematica — Morawetz

Cathleen Morawetz
and the scattering of acoustic waves

Works connected to Donald A. Ludwig

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C. S. Morawetz and D. Ludwig: “An inequality for the reduced wave operator and the justification of geometrical optics,” Comm. Pure Appl. Math. 21 : 2 (March 1968), pp. 187–203. MR 223136 Zbl 0157.18701 article

We present an inequality for the reduced wave operator in the exterior of a star-shaped surface in \( n \)-space, with a Dirichlet boundary condition on the surface and a radiation condition at infinity. This inequality is used to demonstrate the continuous dependence (in a suitable norm) of the solution of a scattering problem upon the boundary data and inhomogeneous term in the differential equation. This basic result is then used together with the results of D. Ludwig [7] to prove that the formal solution of the scattering problem for a convex body, which is given by geometrical optics, is asymptotic to the exact solution. Similar results have been given in two dimensions by V. S. Buslaev [1] and R. Grimshaw [2], using different methods, who also consider the Neumann problem. Unfortunately the methods used here are inapplicable in that case.

Cathleen Morawetzand the scattering of acoustic waves

Works connected to Donald A. Ludwig

Filter the Bibliography List

Cathleen Morawetz
and the scattering of acoustic waves