Abstract
The solvability of the inverse boundary problem with an unknown coefficient dependent on time for the third order pseudoparabolic equation with non-self-adjoint boundary conditions is investigated in the present paper. Here we have introduced the definition of the classical solution of the considered inverse boundary value problem, which is reduced to the system of integral equations by the Fourier method. At first, the existence and uniqueness of the solution of the obtaining system of integral equations is proved by the method of contraction mappings; then the existence and uniqueness of the classical solution of the stated problem is proved.
Highlights
Contemporary problems of natural sciences lead to the need for statement and investigation of the qualitative new problems
As an example we can consider a class of nonlocal problems for the partial differential equations
Researching such kind of problems aroused both theoretical interest and practical necessity and they are still studied actively today. The problems with both nonlocal boundary and initial conditions had previously been studied by many scientists
Summary
Contemporary problems of natural sciences lead to the need for statement and investigation of the qualitative new problems. As an example we can consider a class of nonlocal problems for the partial differential equations. Researching such kind of problems aroused both theoretical interest and practical necessity and they are still studied actively today. The problems with both nonlocal boundary and initial conditions had previously been studied by many scientists. Inverse problems with integral condition of override for pseudoparabolic type of equations had been studied in [8–10]. Existence and uniqueness of the solution of an inverse boundary value problem for the third order pseudoparabolic equation with the integral condition of override is proved in the present paper
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