An existence solution to an identification parameter problem for higher-order partial differential equations

Abstract

The initial-boundary value problem with parameter for higher-order partial differential equations is considered. We study the existence of its solution and also propose a method for finding approximate solutions. We are established a sufficient conditions for the existence and uniqueness of the solution to the identification parameter problem under consideration. Introducing new unknown functions, we reduce the considered problem to an equivalent problem consisting of a nonlocal problem for second-order hyperbolic equations with functional parameters and integral relations. An algorithm for finding an approximate solution to the problem under study is proposed and its convergence is proved. Sufficient conditions for the existence of a unique solution to an equivalent problem with parameters are established. The conditions for the unique solvability of the initial-boundary value problem with parameter for higher-order partial differential equations are obtained in terms of the initial data. Unique solvability to the initial-boundary value problem with parameter for higher-order partial differential equations is interconnected with unique solvability to the nonlocal problem with parameter for secondorder hyperbolic equations.