On nonlinear problems of parabolic type with implicit constitutive equations involving flux

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F21%3A10435827" target="_blank" >RIV/00216208:11320/21:10435827 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=5Y5i8zX3mX" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=5Y5i8zX3mX</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1142/S0218202521500457" target="_blank" >10.1142/S0218202521500457</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On nonlinear problems of parabolic type with implicit constitutive equations involving flux

Popis výsledku v původním jazyce

We study systems of nonlinear partial differential equations of parabolic type, in which the elliptic operator is replaced by the first-order divergence operator acting on a flux function, which is related to the spatial gradient of the unknown through an additional implicit equation. This setting, broad enough in terms of applications, significantly expands the paradigm of nonlinear parabolic problems. Formulating four conditions concerning the form of the implicit equation, we first show that these conditions describe a maximal monotone p-coercive graph. We then establish the global-in-time and large-data existence of a (weak) solution and its uniqueness. To this end, we adopt and significantly generalize Minty&apos;s method of monotone mappings. A unified theory, containing several novel tools, is developed in a way to be tractable from the point of view of numerical approximations.

Název v anglickém jazyce

On nonlinear problems of parabolic type with implicit constitutive equations involving flux

Popis výsledku anglicky

We study systems of nonlinear partial differential equations of parabolic type, in which the elliptic operator is replaced by the first-order divergence operator acting on a flux function, which is related to the spatial gradient of the unknown through an additional implicit equation. This setting, broad enough in terms of applications, significantly expands the paradigm of nonlinear parabolic problems. Formulating four conditions concerning the form of the implicit equation, we first show that these conditions describe a maximal monotone p-coercive graph. We then establish the global-in-time and large-data existence of a (weak) solution and its uniqueness. To this end, we adopt and significantly generalize Minty&apos;s method of monotone mappings. A unified theory, containing several novel tools, is developed in a way to be tractable from the point of view of numerical approximations.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA18-12719S" target="_blank" >GA18-12719S: Thermodynamická a matematická analýza proudění strukturovaných tekutin</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2021

Kód důvěrnosti údajů

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

Název periodika

Mathematical Models and Methods in Applied Sciences

ISSN

0218-2025

e-ISSN

—

Svazek periodika

31

Číslo periodika v rámci svazku

10

Stát vydavatele periodika

SG - Singapurská republika

Počet stran výsledku

52

Strana od-do

2039-2090

Kód UT WoS článku

000722222900004

EID výsledku v databázi Scopus

2-s2.0-85113932175