Loading...
Please wait, while we are loading the content...
Similar Documents
Uniqueness, existence and solution of the direct boundary heat exchange problem for a weakly non-linear temperature conductivity coefficient
| Content Provider | Scilit |
|---|---|
| Author | Tanana, V. P. Markov, B. A. |
| Copyright Year | 2021 |
| Description | Journal: Journal of Physics: Conference Series This work is a preliminary result necessary for the formulation and solution of the inverse heat conduction problem for a weakly quasilinear equation. Nevertheless, the article has independent significance. For the direct heat conduction problem a solution is constructed in the form of a series with a small parameter, the existence of the solution, its uniqueness are proved, and a number of estimates are made - in particular, the rate of decrease of the solution at large times. The solution is built for a medium, part of which has a piecewise constant coefficient of thermal conductivity, and part of the medium has slightly non-linear thermal diffusivity. The construction of a classical solution is impossible due to the discontinuity of the thermal diffusivity, therefore, on the sections of the media the matching conditions are set - the conditions for the continuity of the solution and the condition for the continuity of the heat flux. The solution to the weakly quasilinear equation is constructed in the explicit form of a series with a small parameter, for which uniform convergence is proved. The decreasing of the solution at large times is proved as of time raised to the negative third power. |
| Related Links | https://iopscience.iop.org/article/10.1088/1742-6596/1715/1/012050/pdf |
| ISSN | 17426588 |
| e-ISSN | 17426596 |
| DOI | 10.1088/1742-6596/1715/1/012050 |
| Journal | Journal of Physics: Conference Series |
| Issue Number | 1 |
| Volume Number | 1715 |
| Language | English |
| Publisher | IOP Publishing |
| Publisher Date | 2021-01-01 |
| Access Restriction | Open |
| Subject Keyword | Journal: Journal of Physics: Conference Series Weakly Quasilinear Equation |
| Content Type | Text |
| Resource Type | Article |
| Subject | Physics and Astronomy |
