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Some problems for Helmholtz equations in regions containing an interface
Abstract
The Helmholtz equation plays an important role in the propagation of acoustic waves in an elastic medium. When an elastic medium consists of different layers with different physical properties, the coefficients in the Helmholtz equation may have a jump discontinuity across the interface between the different layers. In this dissertation, four such interface problems for the Helmholtz equations are addressed. Suitable new function spaces are introduced to facilitate the use of Sobolev space methods and boundary integral equation methods to investigate well-posedness issues for the various problems. Both bounded and unbounded domains are considered and both slip and non-slip conditions are treated along the interface. Theorems of existence and uniqueness of the solution are established for each problem.
Subject Area
Mathematics
Recommended Citation
Li, Gongqin, "Some problems for Helmholtz equations in regions containing an interface" (1991). Doctoral Dissertations Available from Proquest. AAI9207425.
https://scholarworks.umass.edu/dissertations/AAI9207425