On the solvability of boundary value problems for multidimensional parabolic equations of fourth order with nonlocal boundary condition of integral form
Abstract:
We investigate solvability of the initial-boundary value problem for linear parabolic equations of fourth order with the boundary conditions connecting the values of solution or conormal the derivative of the solution with values of a certain integral operator from the solution. We prove the theorem of existence and uniqueness of regular solutions.
Keywords:parabolic equation of fourth order, Sobolev space, initial-boundary value problem, continuation method the parameter, a priori estimates, regular solutions.