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dc.contributor.authorCalsina Ballesta, Ángel
dc.contributor.authorSolà-Morales Rubió, Joan de
dc.contributor.authorValència Guitart, Marta
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I
dc.date.accessioned2007-05-03T17:33:27Z
dc.date.available2007-05-03T17:33:27Z
dc.date.issued1997
dc.identifier.urihttp://hdl.handle.net/2117/858
dc.description.abstractThe existence of a (unique) solution of the second order semilinear elliptic equation $$ \sum^{n}_{i,j=0}a_{ij}(x)u_{x_{i}x_{j}}+f(\nabla u,u,x)=0 $$ with $x=(x_{0},x_{1},\dots, x_{n})\in (s_{0},\infty )\times \Omega '$, for a bounded domain $\Omega '$, together with the additional conditions $$ \begin{array}{l} u(x)=0\quad \mbox{for } (x_{1},x_{2},\dots, x_{n})\in\partial \Omega '\\ \\ u(x)=\varphi (x_{1},x_{2},\dots, x_{n})\quad \mbox{for } x_{0}=s_{0}\\ \\ \vert u(x)\vert\quad\mbox{globally bounded} \end{array} $$ is shown to be a well posed problem under some sign and growth restrictions on $f$ and its partial derivatives. It can be seen as an initial value problem, with initial value $\varphi $, in the space ${\cal C}^{0}_{0}(\overline {\Omega '})$ and satisfying the strong order-preserving property. In the case that $a_{ij}$ and $f$ do not depend on $x_{0}$ or are periodic in $x_{0}$ it is shown that the corresponding dynamical system has a compact global attractor. Also, conditions on $f$ are given under which all the solutions tend to zero as $x_{0}$ tends to infinity. Proofs are strongly based on maximum and comparison techniques.
dc.format.extent27 p.
dc.language.isoeng
dc.rightsAttribution-NonCommercial-NoDerivs 2.5 Spain
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/2.5/es/
dc.subject.lcshPartial differential equations
dc.subject.otherEquacions en derivades parcials
dc.titleBounded solutions of some nonlinear elliptic equations in cylindrical domains
dc.typeArticle
dc.subject.lemacEquacions en derivades parcials
dc.contributor.groupUniversitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
dc.subject.amsClassificació AMS::35 Partial differential equations::35J Partial differential equations of elliptic type
dc.subject.amsClassificació AMS::34 Ordinary differential equations::34G Differential equations in abstract spaces
dc.subject.amsClassificació AMS::35 Partial differential equations::35B Qualitative properties of solutions
dc.subject.amsClassificació AMS::47 Operator theory::47H Nonlinear operators and their properties
dc.rights.accessOpen Access
local.personalitzacitaciotrue


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