Boundary condition of the volume potential for an elliptic-parabolic equation with a scalar parameter
Date
2018-06-23
Authors
Kal'menov, Tynysbek
Arepova, Gaukhar
Arepova, Dana
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
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.
Description
Keywords
Boundary conditions, Descent method, Fundamental solutions, Elliptic-parabolic equation, Newton's potential, Volume heat potential, Surface heat potential
Citation
Kal'menov, T. S., Arepova, G. D., & Arepova, D. D. (2018). Boundary condition of the volume potential for an elliptic-parabolic equation with a scalar parameter. <i>Electronic Journal of Differential Equations, 2018</i>(129), pp. 1-14.
Rights
Attribution 4.0 International
Rights Holder
This work is licensed under a Creative Commons Attribution 4.0 International License.