Determination of the coefficient function in a Whitham type nonlinear differential equation with impulse effects

Abstract

In the article, the problems of unique solvability and determination of the redefinition coefficient function in the initial inverse problem for a nonlinear 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 unknown function along the line of characteristics. The unique solvability of the initial inverse problem is proved by the method of successive approximations and contraction mappings. The determination of the unknown coefficient is reduced to solving the nonlinear integral equation. KEYWORDS inverse problem, Whitham type equations, determination of the coefficient function, method of successive approximations, unique solvability.