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Smooth bifurcation for a Signorini problem on a rectangle
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SYSNO ASEP 0377965 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve SCOPUS Title Smooth bifurcation for a Signorini problem on a rectangle Author(s) Eisner, J. (CZ)
Kučera, Milan (MU-W) RID, SAI, ORCID
Recke, L. (DE)Source Title Mathematica Bohemica. - : Matematický ústav AV ČR, v. v. i. - ISSN 0862-7959
Roč. 137, č. 2 (2012), s. 131-138Number of pages 8 s. Language eng - English Country CZ - Czech Republic Keywords Signorini problem ; smooth bifurcation ; variational inequality Subject RIV BA - General Mathematics R&D Projects IAA100190805 GA AV ČR - Academy of Sciences of the Czech Republic (AV ČR) CEZ AV0Z10190503 - MU-W (2005-2011) EID SCOPUS 84870212928 Annotation We study a parameter depending semilinear elliptic PDE on a rectangle with Signorini boundary conditions on a part of one edge and mixed (zero Dirichlet and Neumann) boundary conditions on the rest of the boundary. We describe smooth branches of smooth nontrivial solutions bifurcating from the trivial solution branch in eigenvalues of the linearized problem. In particular, the contact sets of these nontrivial solutions are intervals which change smoothly along the branch. The main tools of the proof are first a certain local equivalence of the unilateral BVP to a system consisting of a corresponding classical BVP and of two scalar equations (which determine the ends of the contact intervals), and secondly an application of the classical Crandall-Rabinowitz type local bifurcation techniques (scaling and application of the Implicit Function Theorem) to that system. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2013
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