SYSTEMS DESCRIBING ELECTROTHERMAL EFFECTS WITH p(x)-LAPLACIAN-LIKE STRUCTURE FOR DISCONTINUOUS VARIABLE EXPONENTS
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F16%3A10332632" target="_blank" >RIV/00216208:11320/16:10332632 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1137/16M1062211" target="_blank" >http://dx.doi.org/10.1137/16M1062211</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/16M1062211" target="_blank" >10.1137/16M1062211</a>
Alternative languages
Result language
angličtina
Original language name
SYSTEMS DESCRIBING ELECTROTHERMAL EFFECTS WITH p(x)-LAPLACIAN-LIKE STRUCTURE FOR DISCONTINUOUS VARIABLE EXPONENTS
Original language description
We consider a coupled system of two elliptic PDEs, where the elliptic term in the first equation shares the properties of the p(x)-Laplacian with discontinuous exponent, while in the second equation we have to deal with an a priori L-1 term on the right-hand side. Such systems are suitable for the description of various electrothermal effects, in particular, those where the non-Ohmic behavior can change dramatically with respect to the spatial variable. We prove the existence of a weak solution under very weak assumptions on the data and also under general structural assumptions on the constitutive equations of the model. The main difficulty consists in the fact that we have to simultaneously overcome two obstacles-the discontinuous variable exponent and the L-1 right-hand side of the heat equation. Our existence proof based on Galerkin approximation is highly constructive and therefore seems to be suitable also for numerical purposes.
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
<a href="/en/project/LL1202" target="_blank" >LL1202: Implicitly constituted material models: from theory through model reduction to efficient numerical methods</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
SIAM Journal on Mathematical Analysis
ISSN
0036-1410
e-ISSN
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Volume of the periodical
48
Issue of the periodical within the volume
5
Country of publishing house
US - UNITED STATES
Number of pages
19
Pages from-to
3496-3514
UT code for WoS article
000387324900015
EID of the result in the Scopus database
2-s2.0-84994091652