Radiative effects for some bidimensional thermoelectric problems
There are two main objectives in this paper. One is to find sufficient conditions to ensure the existence of weak solutions for some bidimensional thermoelectric problems. At the steady-state, these problems consist of a coupled system of elliptic equations of the divergence form, commonly accomplis...
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2016-11-01
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| Series: | Advances in Nonlinear Analysis |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/anona-2015-0128 |
| Summary: | There are two main objectives in this paper.
One is to find sufficient conditions to ensure the existence
of weak solutions for some bidimensional thermoelectric problems.
At the steady-state, these problems consist
of a coupled system of elliptic equations of the divergence form,
commonly accomplished with nonlinear radiation-type conditions
on at least a nonempty part of the boundary of a C1${C^{1}}$ domain.
The model under study takes
the thermoelectric Peltier and Seebeck effects into account,
which describe the Joule–Thomson effect.
The proof method requires a fixed point argument.
To this end, well-determined estimates are our main concern.
The second objective of the paper is
the derivation of explicit W1,p${W^{1,p}}$-estimates
(p>2)${(p>2)}$ for solutions of nonlinear radiation-type problems
in the general n-dimensional space situation,
where the leading coefficient
is assumed to be a discontinuous function on the space
variable.
In particular, the behavior of the leading coefficient is
conveniently explicit on the estimate of any solution. |
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| ISSN: | 2191-9496 2191-950X |