Inverse Problem for Whitham Type Multi-Dimensional Differential Equation with Impulse Effects
A. K. Fayziyev, A. N. Abdullozhonova, T. K. Yuldashev
Abstract
Abstract In the article the questions of unique solvability and determination of the redefinition coefficient function in the inverse problem for multi-dimensional Whitham-type partial differential equation with impulse effects are studied. The modified method of characteristics allows partial differential equations of the first order to be represented as ordinary differential equations that describe the change of an unknown function along the line of characteristics. The unique solvability of the multi-dimensional inverse problem is proved by the method of successive approximations and contraction mappings. The definition of the unknown coefficient is reduced to solving the Volterra integral equation of the first kind.