Inverse Problems of Mathematical Physics

a₁ arbitrary b₁ boundary conditions c₁ calculated Cauchy data Cauchy problem characteristic coefficients components considered continuous function continuously differentiable contracted mapping coordinates corresponding demonstrate Denote derivatives differential equation direct problem domain equalities estimate exists finite formulation Fourier function u(x geophysics H₁(v hence hodograph hyperbolic inequality integral equations integral geometry intercept inverse dynamic inverse kinematic problem inverse problem inverse problem solution investigation known Lemma linear mathematical matrix n²(x obtained operator p₁ parameter plane x3 point xº problem of determining proved respect Russian seismic wave solution to problem solving space SSSR Sturm-Liouville problem sufficient surface system of equations system of integral t)eD t₁ theorem transform transverse waves uniquely defined v₁ valid variable vector velocity W₁ wave waveguides x°ES x₁ zero