On the Analytic Solutions of a Special Boundary Value Problem for a Nonlinear Heat Equation in Polar Coordinates
Publication type: Journal Article
Publication date: 2018-04-01
scimago Q3
SJR: 0.315
CiteScore: 1.0
Impact factor: —
ISSN: 19904789, 19904797
Industrial and Manufacturing Engineering
Applied Mathematics
Abstract
The paper addresses a nonlinear heat equation (the porous medium equation) in the case of a power-law dependence of the heat conductivity coefficient on temperature. The equation is used for describing high-temperature processes, filtration of gases and fluids, groundwater infiltration, migration of biological populations, etc. The heat waves (waves of filtration) with a finite velocity of propagation over a cold background form an important class of solutions to the equation under consideration. A special boundary value problem having solutions of such type is studied. The boundary condition of the problem is given on a sufficiently smooth closed curve with variable geometry. The new theorem of existence and uniqueness of the analytic solution is proved.
Found
Nothing found, try to update filter.
Found
Nothing found, try to update filter.
Top-30
Journals
|
1
2
3
|
|
|
Mathematics
3 publications, 18.75%
|
|
|
Journal of Physics: Conference Series
3 publications, 18.75%
|
|
|
Symmetry
2 publications, 12.5%
|
|
|
Computational Mathematics and Mathematical Physics
2 publications, 12.5%
|
|
|
Journal of Mathematical Sciences
1 publication, 6.25%
|
|
|
Differential Equations
1 publication, 6.25%
|
|
|
Journal of Applied and Industrial Mathematics
1 publication, 6.25%
|
|
|
Siberian Advances in Mathematics
1 publication, 6.25%
|
|
|
Proceedings of the Steklov Institute of Mathematics
1 publication, 6.25%
|
|
|
1
2
3
|
Publishers
|
1
2
3
4
5
6
|
|
|
Pleiades Publishing
6 publications, 37.5%
|
|
|
MDPI
5 publications, 31.25%
|
|
|
IOP Publishing
3 publications, 18.75%
|
|
|
Springer Nature
1 publication, 6.25%
|
|
|
1
2
3
4
5
6
|
- We do not take into account publications without a DOI.
- Statistics recalculated weekly.
Are you a researcher?
Create a profile to get free access to personal recommendations for colleagues and new articles.
Metrics
16
Total citations:
16
Citations from 2024:
2
(12.5%)
Cite this
GOST |
RIS |
BibTex |
MLA
Cite this
GOST
Copy
Kazakov A. L., Kuznetsov P. A. On the Analytic Solutions of a Special Boundary Value Problem for a Nonlinear Heat Equation in Polar Coordinates // Journal of Applied and Industrial Mathematics. 2018. Vol. 12. No. 2. pp. 255-263.
GOST all authors (up to 50)
Copy
Kazakov A. L., Kuznetsov P. A. On the Analytic Solutions of a Special Boundary Value Problem for a Nonlinear Heat Equation in Polar Coordinates // Journal of Applied and Industrial Mathematics. 2018. Vol. 12. No. 2. pp. 255-263.
Cite this
RIS
Copy
TY - JOUR
DO - 10.1134/s1990478918020060
UR - https://doi.org/10.1134/s1990478918020060
TI - On the Analytic Solutions of a Special Boundary Value Problem for a Nonlinear Heat Equation in Polar Coordinates
T2 - Journal of Applied and Industrial Mathematics
AU - Kazakov, A L
AU - Kuznetsov, P. A.
PY - 2018
DA - 2018/04/01
PB - Pleiades Publishing
SP - 255-263
IS - 2
VL - 12
SN - 1990-4789
SN - 1990-4797
ER -
Cite this
BibTex (up to 50 authors)
Copy
@article{2018_Kazakov,
author = {A L Kazakov and P. A. Kuznetsov},
title = {On the Analytic Solutions of a Special Boundary Value Problem for a Nonlinear Heat Equation in Polar Coordinates},
journal = {Journal of Applied and Industrial Mathematics},
year = {2018},
volume = {12},
publisher = {Pleiades Publishing},
month = {apr},
url = {https://doi.org/10.1134/s1990478918020060},
number = {2},
pages = {255--263},
doi = {10.1134/s1990478918020060}
}
Cite this
MLA
Copy
Kazakov, A. L., and P. A. Kuznetsov. “On the Analytic Solutions of a Special Boundary Value Problem for a Nonlinear Heat Equation in Polar Coordinates.” Journal of Applied and Industrial Mathematics, vol. 12, no. 2, Apr. 2018, pp. 255-263. https://doi.org/10.1134/s1990478918020060.