Asymptotic analysis of a nonlinear partial differential equation in a semicylinder
2004 (English)Licentiate thesis, monograph (Other academic)
We study small solutions of a nonlinear partial differential equation in a semi-infinite cylinder. The asymptotic behaviour of these solutions at infinity isdetermined. First, the equation under the Neumann boundary condition is studied. We show that any solution small enough either vanishes at infinity ortends to a nonzero periodic solution of a nonlinear ordinary differential equation. Thereafter, the same equation under the Dirichlet boundary condition is studied, but now the nonlinear term and right-hand side are slightly more general than in the Neumann problem. Here, an estimate of the solution in terms of the right-hand side of the equation is given. If the equation is homogeneous, then every solution small enough tends to zero. Moreover, if the cross-section is star-shaped and the nonlinear term in the equation is subject to some additional constraints, then every bounded solution of the homogeneous Dirichlet problem vanishes at infinity. An estimate for the solution is given.
Place, publisher, year, edition, pages
Linköping: Linköpings universitet , 2004. , 51 p.
Linköping Studies in Science and Technology. Thesis, ISSN 0280-7971 ; 1112
IdentifiersURN: urn:nbn:se:liu:diva-23692Local ID: 3191ISBN: 91-7373-998-7OAI: oai:DiVA.org:liu-23692DiVA: diva2:244007
2004-09-22, Glashuset, Hus B, Linköpings Universitet, Linköping, 10:15 (Swedish)
Shahgolian, Henrik, Professor