An Inverse Problem in the Presence

of a mixed Boundary


F.D. Zaman*


Department of Mathematical Sciences

King Fahd University of Petroleum & Minerals 








The inverse problems involving parameter identification have attracted considerable attention during recent years. The problem has been studies by various authors in seismic and acoustic context. These studies focus on the physical boundary of the medium satisfying one kind of boundary condition. We consider a model in which identification of an inhomogeinity is sought in the presence of mixed boundary conditions: the boundary consisting of two parts with different impedance coefficients. The Wiener-Hopf method provides with the solution of the mixed boundary value problem (direct scattering problem), while the inverse problem of the determination of inhomogeneity is reduced to the Fredholm integral equation of the first kind. The procedure can be applied to recover acoustic speed variation in an ocean due to a pollutant with non-homogeneous seabed seabed  or in the atmosphere in the presence of mixed conditions at the ground.


*In collaboration with Khaled Masood, Hafr Al-Baten Community College