In this paper, we consider the system of second-order mixed type equations. Theorems of uniqueness and conditional stability in the set of correctness are proven. The approximate solution is constructed by the method of regularization and by the quasi-inverse method.Keywords: system of equations, boundary value problem, ill-posed problem, a priori estimate, theorem of the uniqueness, conditional stability, set of correctness, approximate solution, regularization.
The criterion of uniqueness of a solution of the problem with periodicity and nonlocal and boundary conditions is established by the spectral analysis for a fourth-order mixed-type equation in a rectangular region. When constructing a solution in the form of the sum of a series, we use the completeness in the space L_2, the system of eigenfunctions of the corresponding problem orthogonally conjugate. When proving the convergence of a series, the problem of small denominators arises. Under some conditions imposed on the parameters of the data of the problem and given functions, the stability of the solution is proved.
In this paper, we consider a system of equations of mixed type and with changing time direction. It is proved that solution of the system is not stable depend from the variation of the data. Theorems of uniqueness and conditional stability proved. The approximate solution constructed and numerical results are given.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.