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Two-Dimensional and Three-Dimensional Thermal Structures in a Medium with Nonlinear Thermal Conductivity
| Content Provider | Semantic Scholar |
|---|---|
| Author | Kurkina, E. S. |
| Copyright Year | 2005 |
| Abstract | The article considers self-similar solutions of the nonlinear heat equation with a three-dimensional source that evolve in a blow-up setting. The self-similar problem is a boundary-value problem for a nonlinear equation of elliptical type that has a nonunique solution. We investigate the eigenfunction spectrum of the self-similar problem in two- and three-dimensional space. The problem is solved on a grid by Newton’s iteration method. The implementation of Newton’s method requires analysis of a linearized equation and construction of initial approximations. The eigenfunctions are continued in a parameter. Structures of various symmetry are obtained. New types of multidimensional structures are observed: these are multiply connected three-dimensional heat localization regions. |
| Starting Page | 257 |
| Ending Page | 278 |
| Page Count | 22 |
| File Format | PDF HTM / HTML |
| DOI | 10.1007/s10598-005-0023-8 |
| Volume Number | 16 |
| Alternate Webpage(s) | https://page-one.springer.com/pdf/preview/10.1007/s10598-005-0023-8 |
| Alternate Webpage(s) | https://doi.org/10.1007/s10598-005-0023-8 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
