Instability of spatially - Periodic states for a family of semilinear PDE's on an infinite strip

Mathematische Nachrichten

Volumn 179, Issue , 1996, Pages 5-25

  Bridges, Thomas J ^a   Mielke, Alexander ^b  

^a UNIVERSITY OF SURREY   (United Kingdom)

^b Leibniz Universität Hannover   (Germany)

Author keywords

Center manifold; Hamiltonian structure; Reduced instability; Spatial dymanics

Indexed keywords

EID: 0012231761     PISSN: 0025584X     EISSN: None     Source Type: Journal    
DOI: 10.1002/mana.19961790102     Document Type: Article

References (9)

1. T. J. BRIDGES, T. J., and MIELKE, A.: A Proof of the Benjamin - Feir Instability, Archive for Rational Mechanics and Analysis, 133 (1995), 145-198
2. BRIDGES, T. J., and ROWLANDS, G.: Instability of Spatially Quasiperiodic States of the Ginzburg-Landau Equation, Proc. Roy. Soc. Lond. A444 (1994), pp. 347-62
3. INFELD, E., and ROWLANDS, G.: Nonlinear Waves, Solitons and Chaos, Cambridge University Press, 1990
4. KIRCHGÄSSNER, K.: Wave Solutions of Reversible Systems and Applications, J. Diff. Eqns. 45 (1982), pp. 113-27
5. MIELKE. A. Reduction of Quasilinear Elliptic Equations in Cylindrical Domains with Applications, Math. Meth. Applied Sci. 10 (1988) pp. 51-66
6. MIELKE, A.: Hamiltonian and Lagrangian Flows on Center Manifolds, Lect. Notes in Maths. 1489, Springer-Verlag: Berlin
7. MIELKE, A.: Essential Manifolds for an Elliptic Problem in an Infinite Strip, J. Diff. Eqns. 110 (1994), pp. 322-55
8. MIELKE, A.: A New Approach to Sideband Instabilities Using the Principle of Reduced Instability. In "Nonlinear Dynamics and Pattern Formation in the Natural Environment. A. Doelman, A. van Harten (eds). Pitman Research Notes in Mathematics, 1995" pp. 206-222
9. MIELKE, A.: Mathematical Analysis of Sideband Instabilites with Application to Rayleigh -Bénard Convection, J. Nonlinear Science. Submitted 1995.