Multidimensional Inverse Problems for Differential Equations

apply arbitrary arrive assume belong boundary conditions bounded chapter circle coefficients consider construct continuous function convergent coordinates corresponding curves defined Denote derive determine determining a function differential equation direction domain earth's ellipses ellipsoid of revolution exists expression family of curves fixed formula functions u(r geometry given GREEN'S function half-plane half-space heat Hence hold implies inequality integral equation Introduce inverse problem inversion formula known linearized method moments multidimensional namely Notes obtain operator origin parameters plane polar problem for equation problem of determining propagation properties proved question radius reduced relations represented respect right-hand side satisfies similar solution to equation space spheres Substituting sufficient take FOURIER transforms telegraph equation theorem unique uniqueness theorem unit vanishes variables waves