| Title:
|
Weak solutions to a time-dependent heat equation with nonlocal radiation boundary condition and arbitrary $p$-summable right-hand side (English) |
| Author:
|
Druet, Pierre-Etienne |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
55 |
| Issue:
|
2 |
| Year:
|
2010 |
| Pages:
|
111-149 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We consider a model for transient conductive-radiative heat transfer in grey materials. Since the domain contains an enclosed cavity, nonlocal radiation boundary conditions for the conductive heat-flux are taken into account. We generalize known existence and uniqueness results to the practically relevant case of lower integrable heat-sources, and of nonsmooth interfaces. We obtain energy estimates that involve only the $L^p$ norm of the heat sources for exponents $p$ close to one. Such estimates are important for the investigation of models in which the heat equation is coupled to Maxwell's equations or to the Navier-Stokes equations (dissipative heating), with many applications such as crystal growth. (English) |
| Keyword:
|
radiative heat transfer |
| Keyword:
|
nonlinear parabolic equation |
| Keyword:
|
nonlocal boundary condition |
| Keyword:
|
right-hand side in $L^1$ |
| MSC:
|
35D05 |
| MSC:
|
35D30 |
| MSC:
|
35K05 |
| MSC:
|
35K15 |
| MSC:
|
35K20 |
| MSC:
|
35K55 |
| MSC:
|
35K59 |
| MSC:
|
80A20 |
| idZBL:
|
Zbl 1224.35057 |
| idMR:
|
MR2600939 |
| DOI:
|
10.1007/s10492-010-0005-9 |
| . |
| Date available:
|
2010-07-20T13:35:13Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140391 |
| . |
| Reference:
|
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| Reference:
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