Computation of Morse decompositions for semilinear elliptic PDEs

DOI10.1002/num.7zbMath0989.65137OpenAlexW2136296965MaRDI QIDQ2725058

Michael W. Smiley, Changbum Chun

Publication date: 15 July 2002

Published in: Numerical Methods for Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/num.7

zbMATH Keywords

stabilityconvergencenumerical examplesMorse indexLyapunov-Schmidt reductionsemilinear elliptic problemsubdivision algorithmbifurcation function

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Bifurcations in context of PDEs (35B32) Numerical bifurcation problems (65P30) Bifurcation problems for infinite-dimensional Hamiltonian and Lagrangian systems (37K50)

Related Items (4)

Numerical analysis of semilinear elliptic equations with finite spectral interaction ⋮ Optimal order error estimates for finite element approximations of a bifurcation function ⋮ An algorithm for finding all solutions of a nonlinear system ⋮ An approximate bifurcation function and existence of solutions for semilinear elliptic PDEs

Cites Work

• Unnamed Item
• Unnamed Item
• Finite dimensional approximation of nonlinear problems. II: Limit points
• Finite dimensional approximation of nonlinear problems. III: Simple bifurcation points
• Lower semicontinuity of attractors of gradient systems and applications
• A numerical study of spontaneous bifurcation
• Finite dimensional approximation of nonlinear problems. I: Branches of nonsingular solutions
• A principle of reduced stability for reaction-diffusion equations
• On a numerical Lyapunov-Schmidt method for operator equations
• Numerical Liapunov-Schmidt spectral method for \(k\)-determined problems
• A bifurcation problem for a nonlinear partial differential equation of parabolic type^†
• Elliptic Partial Differential Equations of Second Order
• The global attractor for a Chafee-Infante problem with source term
• Approximation of the bifurcation function for elliptic boundary value problems

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