ON A INITIAL - BOUNDARY VALUE PROBLEM FOR THE PARABOLIC EQUATIONS WITH THE INITIAL OPERATORS OF FRACTIONAL ORDER

Abstract

In the present paper, we study an initial-boundary problem for the parabolic equation  with general elliptic operator and fractional initial conditions. Here   non negative elliptic operator which defined in any  N  dimensional domain  with the smooth boundary. We prove the existence and uniqueness of the solution of the problem. We found orthogonality and smoothness conditions on the initial function, which guarantee both the existence and uniqueness of the classical solutions.