Generic bifurcation of steady-state solutions

DOI10.1016/0022-0396(84)90172-4zbMath0488.58015OpenAlexW2009756463MaRDI QIDQ1166179

Arthur G. Wassermann, J. A. Smoller

Publication date: 1984

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/2027.42/24837

zbMATH Keywords

Sard's theoremtime mapMorse functiongeneric bifurcation of steady-state solutionsordinary differential equation with homogeneous Dirichlet or Neumann boundary conditions

Mathematics Subject Classification ID

Initial-boundary value problems for second-order parabolic equations (35K20) Singularities of differentiable mappings in differential topology (57R45) Bifurcations in context of PDEs (35B32) Local and nonlocal bifurcation theory for dynamical systems (37G99)

Related Items (11)

Convergence of the wave equation damped on the interior to the one damped on the boundary ⋮ Generic properties of equilibria of reaction-diffusion equations with variable diffusion ⋮ Noncompact global attractors for scalar reaction-diffusion equations ⋮ Generic hyperbolicity for scalar parabolic equations ⋮ Generic hyperbolicity in one-dimensional reaction- diffusion equations with general boundary conditions ⋮ Connecting orbits in scalar reaction diffusion equations. II: The complete solution ⋮ A permutation related to the dynamics of a scalar parabolic PDE ⋮ Stationary patterns to diffusion problems ⋮ Generic hyperbolicity of equilibria and periodic orbits of the parabolic equation on the circle ⋮ Lower semicontinuity of attractors of gradient systems and applications ⋮ Continuity of attractors

Cites Work

• Unnamed Item
• Generic properties of stationary state solutions of reaction-diffusion equations
• Global bifurcation of steady-state solutions
• Integral averaging and bifurcation
• Non-degenerate solutions of boundary-value problems

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