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 |
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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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