The second initial-boundary value problem with integral displacement for second-order hyperbolic and parabolic equations

Abstract

In this paper, we study the solvability of some non-local analogs of the second initial-boundary value problem for multidimensional hyperbolic and parabolic equations of the second order. We prove the existence and uniqueness theorems of regular solutions (which have all Sobolev generalized derivatives that are summable with a square and are included in the equation). Some generalization and amplification of the obtained results are also given.

Keywords

• hyperbolic equations
• parabolic equations
• integral boundary conditions
• nonlocal problems
• integral conditions
• regular solutions
• uniqueness
• existence