Electron. J. Differential Equations, Vol. 2018 (2018), No. 129, pp. 1-14.

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

Tynysbek Sh. Kal'menov, Gaukhar D. Arepova, Dana D. Arepova

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.

Submitted January 7, 2018. Published June 23, 2018.
Math Subject Classifications: 35M12.
Key Words: Boundary conditions; descent method; fundamental solutions, Elliptic-parabolic equation; Newton's potential; volume heat potential; surface heat potential

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Tynysbek Sh. Kal'menov
Institute of Mathematics and Mathematical Modelling
125 Pushkin street
050010 Almaty, Kazakhstan
email: kalmenov.t@mail.ru
Gaukhar D. Arepova
Institute of Mathematics and Mathematical Modelling
125 Pushkin street
050010 Almaty, Kazakhstan
email: arepovag@mail.ru
  Dana D. Arepova
Institute of Mathematics and Mathematical Modelling
125 Pushkin street
050010 Almaty, Kazakhstan
email: danaarepova@gmail.com

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