Direction and stability of bifurcating solutions for a Signorini problem

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60076658%3A12310%2F15%3A43889018" target="_blank" >RIV/60076658:12310/15:43889018 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/67985840:_____/15:00437684 RIV/49777513:23520/15:43928430

Výsledek na webu

<a href="http://www.sciencedirect.com/science/article/pii/S0362546X14003228" target="_blank" >http://www.sciencedirect.com/science/article/pii/S0362546X14003228</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.na.2014.09.032" target="_blank" >10.1016/j.na.2014.09.032</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Direction and stability of bifurcating solutions for a Signorini problem

Popis výsledku v původním jazyce

The equation Delta u+lambda u+ g(lambda, u)u = 0 is considered in a bounded domain in R-2 with a Signorini condition on a straight part of the boundary and with mixed boundary conditions on the rest of the boundary. It is assumed that g(lambda, 0) = 0 for lambda is an element of R, lambda is a bifurcation parameter. A given eigenvalue of the linearized equation with the same boundary conditions is considered. A smooth local bifurcation branch of non-trivial solutions emanating at lambda(0) from trivialsolutions is studied. We show that to know a direction of the bifurcating branch it is sufficient to determine the sign of a simple expression involving the corresponding eigenfunction u(0). In the case when lambda(0) is the first eigenvalue and the branch goes to the right, we show that the bifurcating solutions are asymptotically stable in W-1,W-2-norm. The stability of the trivial solution is also studied and an exchange of stability is obtained.

Název v anglickém jazyce

Direction and stability of bifurcating solutions for a Signorini problem

Popis výsledku anglicky

The equation Delta u+lambda u+ g(lambda, u)u = 0 is considered in a bounded domain in R-2 with a Signorini condition on a straight part of the boundary and with mixed boundary conditions on the rest of the boundary. It is assumed that g(lambda, 0) = 0 for lambda is an element of R, lambda is a bifurcation parameter. A given eigenvalue of the linearized equation with the same boundary conditions is considered. A smooth local bifurcation branch of non-trivial solutions emanating at lambda(0) from trivialsolutions is studied. We show that to know a direction of the bifurcating branch it is sufficient to determine the sign of a simple expression involving the corresponding eigenfunction u(0). In the case when lambda(0) is the first eigenvalue and the branch goes to the right, we show that the bifurcating solutions are asymptotically stable in W-1,W-2-norm. The stability of the trivial solution is also studied and an exchange of stability is obtained.

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/GA13-00863S" target="_blank" >GA13-00863S: Semilineární a kvazilineární diferenciální rovnice: existence a násobnost řešení</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2015

Kód důvěrnosti údajů

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

Název periodika

Nonlinear Analysis: Theory, Methods &amp; Application

ISSN

0362-546X

e-ISSN

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Svazek periodika

113

Číslo periodika v rámci svazku

JAN 2015

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

15

Strana od-do

357-371

Kód UT WoS článku

000345687300020

EID výsledku v databázi Scopus

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