On the strong comparison principle for degenerate elliptic problems with convection

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F22%3A43965742" target="_blank" >RIV/49777513:23520/22:43965742 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/pii/S0022247X22002815" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0022247X22002815</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jmaa.2022.126267" target="_blank" >10.1016/j.jmaa.2022.126267</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On the strong comparison principle for degenerate elliptic problems with convection

Popis výsledku v původním jazyce

The weak and strong comparison principles (WCP and SCP, respectively) are investigated for quasilinear elliptic boundary value problems with the p-Laplacian in one space dimension, Δp(u) =d/dx(|u&apos;|p−2u&apos;). We treat the “degenerate” case of 2 &lt;p &lt;∞ and allow also for the nontrivial convection velocity b :[−1, 1] →R in the underlying domain Ω =(−1, 1). We establish the WCP under a rather general, “natural sufficient condition” on the convection velocity, b(x), and the reaction function, ϕ(x, u). Furthermore, we establish also the SCP under a number of various additional hypotheses. In contrast, with these hypotheses being violated, we construct also a few rather natural counterexamples to the SCP and discuss their applications to an interesting classical problem of fluid flow in porous medium, “seepage flow of fluids in inclined bed”. Our methods are based on a mixture of classical and new techniques.

Název v anglickém jazyce

On the strong comparison principle for degenerate elliptic problems with convection

Popis výsledku anglicky

The weak and strong comparison principles (WCP and SCP, respectively) are investigated for quasilinear elliptic boundary value problems with the p-Laplacian in one space dimension, Δp(u) =d/dx(|u&apos;|p−2u&apos;). We treat the “degenerate” case of 2 &lt;p &lt;∞ and allow also for the nontrivial convection velocity b :[−1, 1] →R in the underlying domain Ω =(−1, 1). We establish the WCP under a rather general, “natural sufficient condition” on the convection velocity, b(x), and the reaction function, ϕ(x, u). Furthermore, we establish also the SCP under a number of various additional hypotheses. In contrast, with these hypotheses being violated, we construct also a few rather natural counterexamples to the SCP and discuss their applications to an interesting classical problem of fluid flow in porous medium, “seepage flow of fluids in inclined bed”. Our methods are based on a mixture of classical and new techniques.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

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

Rok uplatnění

2022

Kód důvěrnosti údajů

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

Název periodika

Journal of Mathematical Analysis and Applications

ISSN

0022-247X

e-ISSN

1096-0813

Svazek periodika

514

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

21

Strana od-do

1-21

Kód UT WoS článku

000832060500018

EID výsledku v databázi Scopus

2-s2.0-85130887430