THERMISTOR SYSTEMS OF p(x)-LAPLACE-TYPE WITH DISCONTINUOUS EXPONENTS VIA ENTROPY SOLUTIONS
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F17%3A10367388" target="_blank" >RIV/00216208:11320/17:10367388 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.3934/dcdss.2017035" target="_blank" >http://dx.doi.org/10.3934/dcdss.2017035</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.3934/dcdss.2017035" target="_blank" >10.3934/dcdss.2017035</a>
Alternative languages
Result language
angličtina
Original language name
THERMISTOR SYSTEMS OF p(x)-LAPLACE-TYPE WITH DISCONTINUOUS EXPONENTS VIA ENTROPY SOLUTIONS
Original language description
We show the existence of solutions to a system of elliptic PDEs, that was recently introduced to describe the electrothermal behavior of organic semiconductor devices. Here, two difficulties appear: (i) the elliptic term in the current-flow equation is of p (x)-Laplacian-type with discontinuous exponent p, which limits the use of standard methods, and (ii) in the heat equation, we have to deal with an a priori L-1 term on the right hand side describing the Joule heating in the device. We prove the existence of a weak solution under very weak assumptions on the data. Our existence proof is based on Schauder's fixed point theorem and the concept of entropy solutions for the heat equation. Here, the crucial point is the continuous dependence of the entropy solutions on the data of the problem.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
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
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Discrete and Continuous Dynamical Systems - Series S
ISSN
1937-1632
e-ISSN
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Volume of the periodical
10
Issue of the periodical within the volume
4
Country of publishing house
US - UNITED STATES
Number of pages
17
Pages from-to
697-713
UT code for WoS article
000401080600005
EID of the result in the Scopus database
2-s2.0-85018389252