Reduction of spectral problem of Cauchy-Riemann operator with homogeneous boundary conditions to an integral equation

Subject Applied Mathematics
Title Reduction of spectral problem of Cauchy-Riemann operator with homogeneous boundary conditions to an integral equation
Author(s) N.S.Imanbayev
Keywords Differential operation of the Cauchy-Riemann, elliptic operators
Abstract In this paper the problem on the eigenvalues of the Cauchy-Riemann operator with homogeneous boundary conditions is reduced to an integral equation.

MIXED PROBLEM FOR A DIFFERENTIAL EQUATION WITH INVOLUTION UNDER BOUNDARY CONDITIONS OF GENERAL FORM

Subject Applied Mathematics
Title MIXED PROBLEM FOR A DIFFERENTIAL EQUATION WITH INVOLUTION UNDER BOUNDARY CONDITIONS OF GENERAL FORM
Author(s) M.A.Sadybekov,A.M.Sarsenbi
Keywords mixed problem, involution, the Fourier method, the Riesz basis, biorthogonal decomposition, classical solution
Abstract To solve the mixed problem for a partial differential equation with involution and a symmetric potential there was found an explicit analytical representation by the Fourier method. The problem was considered under general boundary conditions with constant coefficients by a space variable. At the same we used the methods for avoiding the termwise differentiation of a functional series and applying the minimal conditions on initial data of the problem.