Reduction of quasilinear elliptic equations in cylindrical domains with applications
- 1 February 1988
- journal article
- research article
- Published by Wiley in Mathematical Methods in the Applied Sciences
- Vol. 10 (1) , 51-66
Abstract
For certain types of semilinear partial differential equations in a cylindrical domain small bounded solutions are known to lie on a so‐called centre manifold of finite dimension. In this paper we prove the result for quasilinear partial differential equations of elliptic and parabolic type.Possible applications include free surface waves and problems in non‐linear elasticity. Here we investigate, pars pro toto, the stationary inviscid potential flow in a channel with a free surface and an obstacle at the bottom.Keywords
This publication has 9 references indexed in Scilit:
- ber maximaleL p-Regularit t f r Differentialgleichungen in Banach- und Hilbert-R umenMathematische Annalen, 1987
- Steady flows of inviscid fluids under localized perturbationsJournal of Differential Equations, 1986
- A reduction principle for nonautonomous systems in infinite-dimensional spacesJournal of Differential Equations, 1986
- A variational approach to surface solitary wavesJournal of Differential Equations, 1984
- Zentrumsmannigfaltigkeiten bei elliptischen DifferentialgleichungenMathematische Nachrichten, 1984
- Wave-solutions of reversible systems and applicationsJournal of Differential Equations, 1982
- Geometric Theory of Semilinear Parabolic Equations1981
- Internal waves of finite amplitude and permanent formJournal of Fluid Mechanics, 1966
- The existence of solitary wavesCommunications on Pure and Applied Mathematics, 1954