A strong solution of a high-order mixed type partial differential equation with integral conditions

Abstract

In this article, we study a mixed problem with integral boundary conditions for a high-order partial differential equation of mixed type. We prove the existence and uniqueness of a strong solution. The proof is based on energy inequality and on the density of the range of the operator generated by the considered problem.

Keywords:

• integral boundary conditions
• energy inequalities
• equation of mixed type

AMS (MOS) Subject Classifications:

• 35B45
• 35G10
• 35M10