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Bounded solutions of some nonlinear elliptic equations in cylindrical domains
dc.contributor.author | Calsina Ballesta, Ángel |
dc.contributor.author | Solà-Morales Rubió, Joan de |
dc.contributor.author | València Guitart, Marta |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I |
dc.date.accessioned | 2007-05-03T17:33:27Z |
dc.date.available | 2007-05-03T17:33:27Z |
dc.date.issued | 1997 |
dc.identifier.uri | http://hdl.handle.net/2117/858 |
dc.description.abstract | The 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.extent | 27 p. |
dc.language.iso | eng |
dc.rights | Attribution-NonCommercial-NoDerivs 2.5 Spain |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/2.5/es/ |
dc.subject.lcsh | Partial differential equations |
dc.subject.other | Equacions en derivades parcials |
dc.title | Bounded solutions of some nonlinear elliptic equations in cylindrical domains |
dc.type | Article |
dc.subject.lemac | Equacions en derivades parcials |
dc.contributor.group | Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions |
dc.subject.ams | Classificació AMS::35 Partial differential equations::35J Partial differential equations of elliptic type |
dc.subject.ams | Classificació AMS::34 Ordinary differential equations::34G Differential equations in abstract spaces |
dc.subject.ams | Classificació AMS::35 Partial differential equations::35B Qualitative properties of solutions |
dc.subject.ams | Classificació AMS::47 Operator theory::47H Nonlinear operators and their properties |
dc.rights.access | Open Access |
local.personalitzacitacio | true |
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