Boundary condition of the volume potential for an elliptic-parabolic equation with a scalar parameter

Abstract

Using the descent method for the fundamental solution of the heat equation with a scalar parameter, we find the fundamental solution of the multidimensional Helmholtz equation in an explicit form. We also find a boundary condition of the volume potential for an elliptic-parabolic equation with a scalar parameter. In turn, this condition allows us to construct and study a new correct nonlocal (initial) Bitsadze-Samarsky type problem for an elliptic-parabolic equation with a scalar parameter.

Keywords

• Boundary conditions
• descent method
• fundamental solutions,
• Elliptic-parabolic equation
• Newton's potential
• volume heat potential
• surface heat potential