EXISTENCE OF A SOLUTION TO A MIXED PROBLEM FOR A PARABOLIC EQUATION IN THE SENSE OF SHILOV

Summary: Mixed problem for the fourth order ordinary differential equation with general boundary conditions is considered in present paper. Soluion of the problem is found by the residue method. According to the scheame of this method the mixed problem is divided by two auxiliary- specrtal and Cauchy problems. After researching these two problems, solution of the considering mixed problem is found by residue series. It is shown , that solution of considering mixed problem surround not only parabolic equations in the sense of Shilov, but also wider classes of equations.