Mathematics

Inverse problem for the equation of the mixed type with nonlocal boundary condition

N. V. Martemyanova

Dept. of Mathematical Analysis, Samara State Academy of Social Sciences and Humanities, Samara, 443090, Russian Federation

Abstract: The nonlocal boundary problem is studied in the rectangular region for the equation of the mixed type with the unknown right part. The criterion of the uniqueness of solution of this inverse problem is established. Solution is constructed as a sum of biorthogonal series on the systems of root functions of the corresponding mutually adjoint problems on their own values.

Keywords: inverse problem, equation of the mixed type, spectral method, uniqueness, existence.

UDC: 517.95

Received: 15.05.2010
Revised: 15.05.2010