SYSTEMS DESCRIBING ELECTROTHERMAL EFFECTS WITH p(x)-LAPLACIAN-LIKE STRUCTURE FOR DISCONTINUOUS VARIABLE EXPONENTS

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

SYSTEMS DESCRIBING ELECTROTHERMAL EFFECTS WITH p(x)-LAPLACIAN-LIKE STRUCTURE FOR DISCONTINUOUS VARIABLE EXPONENTS

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

SYSTEMS DESCRIBING ELECTROTHERMAL EFFECTS WITH p(x)-LAPLACIAN-LIKE STRUCTURE FOR DISCONTINUOUS VARIABLE EXPONENTS

Popis výsledku anglicky

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.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/LL1202" target="_blank" >LL1202: Materiály s implicitními konstitutivními vztahy: Od teorie přes redukci modelů k efektivním numerickým metodám</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2016

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

SIAM Journal on Mathematical Analysis

ISSN

0036-1410

e-ISSN

—

Svazek periodika

48

Číslo periodika v rámci svazku

5

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

19

Strana od-do

3496-3514

Kód UT WoS článku

000387324900015

EID výsledku v databázi Scopus

2-s2.0-84994091652