Inverse boundary value problem for the pseudoparabolic equation of third orderwith periodic and integral conditions

摘要

We analyze the solvability of the inverse problem with an unknowncoefficient depended on time for the pseudoparabolic equation of thirdorder with periodic and integral conditions.The initial problem is reducedto an equivalent problem. With the help of the Fourier method,the equivalent problem is reduced to a system of integral equations.The existence and uniqueness of the solution of the integral equations isproved. The obtained solution of the integral equations is also the onlysolution to the equivalent problem. Basing on the equivalence of theproblems, the theorem of the existence and uniqueness of the classicalsolutions of the original problem is proved.