Nonuniqueness and multi-bump solutions in parabolic problems with the p-Laplacian

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F16%3A43928171" target="_blank" >RIV/49777513:23520/16:43928171 - isvavai.cz</a>

Výsledek na webu

<a href="http://www.sciencedirect.com/science/article/pii/S0022039615004702" target="_blank" >http://www.sciencedirect.com/science/article/pii/S0022039615004702</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jde.2015.09.015" target="_blank" >10.1016/j.jde.2015.09.015</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Nonuniqueness and multi-bump solutions in parabolic problems with the p-Laplacian

Popis výsledku v původním jazyce

The validity of the weak and strong comparison principles for degenerate parabolic partial differential equations with the p-Laplace operator is investigated for p>2. This problem is reduced to the comparison of the trivial solution (IDENTICAL TO0, by hypothesis) with a nontrivial nonnegative solution u(x,t). The problem is closely related also to the question of uniqueness of a nonnegative solution via the weak comparison principle. In this article, realistic counterexamples to the uniqueness of a nonnegative solution, the weak comparison principle, and the strong maximum principle are constructed with a nonsmooth reaction function that satisfies neither a Lipschitz nor an Osgood standard "uniqueness" condition. Nonnegative multi-bump solutions with spatially disconnected compact supports and zero initial data are constructed between sub- and supersolutions that have supports of the same type.

Název v anglickém jazyce

Nonuniqueness and multi-bump solutions in parabolic problems with the p-Laplacian

Popis výsledku anglicky

The validity of the weak and strong comparison principles for degenerate parabolic partial differential equations with the p-Laplace operator is investigated for p>2. This problem is reduced to the comparison of the trivial solution (IDENTICAL TO0, by hypothesis) with a nontrivial nonnegative solution u(x,t). The problem is closely related also to the question of uniqueness of a nonnegative solution via the weak comparison principle. In this article, realistic counterexamples to the uniqueness of a nonnegative solution, the weak comparison principle, and the strong maximum principle are constructed with a nonsmooth reaction function that satisfies neither a Lipschitz nor an Osgood standard "uniqueness" condition. Nonnegative multi-bump solutions with spatially disconnected compact supports and zero initial data are constructed between sub- and supersolutions that have supports of the same type.

Druh

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

CEP obor

BA - Obecná matematika

OECD FORD obor

—

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach<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

JOURNAL OF DIFFERENTIAL EQUATIONS

ISSN

0022-0396

e-ISSN

—

Svazek periodika

260

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

19

Strana od-do

"991?1009"

Kód UT WoS článku

—

EID výsledku v databázi Scopus

—