Connecting orbits in scalar reaction diffusion equations. II: The complete solution
From MaRDI portal
Publication:913113
DOI10.1016/0022-0396(89)90180-0zbMath0699.35144OpenAlexW2160215365MaRDI QIDQ913113
Pavol Brunovský, Bernold Fiedler
Publication date: 1989
Published in: Journal of Differential Equations (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/0022-0396(89)90180-0
Related Items (54)
Characterization of the attractor for nonautonomous reaction-diffusion equations with discontinuous nonlinearity ⋮ Schoenflies spheres as boundaries of bounded unstable manifolds in gradient Sturm systems ⋮ Estimates for a class of slowly non-dissipative reaction-diffusion equations ⋮ Limiting classification on linearized eigenvalue problems for 1-dimensional Allen-Cahn equation. II: Asymptotic profiles of eigenfunctions. ⋮ Order structures and the heat equation ⋮ Sturm 3-ball global attractors 3: examples of Thom-Smale complexes ⋮ Noncompact global attractors for scalar reaction-diffusion equations ⋮ Dynamics as a mechanism preventing the formation of finer and fine microstructure ⋮ Sturm attractors for quasilinear parabolic equations ⋮ On monotonicity of solutions to mixed problems for weakly coupled cooperative parabolic systems ⋮ Behavior of solutions to nonlinear parabolic equations at large time ⋮ Attractors of viscous balance laws: Uniform estimates for the dimension ⋮ Hyperbolic periodic orbits in nongradient systems and small-noise-induced metastable transitions ⋮ STRUCTURE OF THE ATTRACTOR OF THE CAHN–HILLIARD EQUATION ON A SQUARE ⋮ Sturm attractors for fully nonlinear parabolic equations ⋮ A product theorem for connection matrices and the structure of connecting orbits ⋮ Spatially monotone homoclinic orbits in nonlinear parabolic equations of super-fast diffusion type ⋮ Limiting grow-up behavior for a one-parameter family of dissipative PDEs ⋮ Entire solutions and a Liouville theorem for a class of parabolic equations on the real line ⋮ Representation and asymptotic formulas for \(1\)-dimensional linearized eigenvalue problems with Dirichlet boundary condition ⋮ Meanders, zero numbers and the cell structure of Sturm global attractors ⋮ Homoclinic bifurcation at resonant eigenvalues ⋮ A Poincaré-Bendixson theorem for scalar reaction diffusion equations ⋮ A permutation characterization of Sturm global attractors of Hamiltonian type ⋮ Complicated dynamics in scalar semilinear parabolic equations in higher space dimension ⋮ Nonlinear Sturm global attractors: unstable manifold decompositions as regular CW-complexes ⋮ A permutation related to the dynamics of a scalar parabolic PDE ⋮ Properties of the attractor of a scalar parabolic PDE ⋮ The attractor of the scalar reaction diffusion equation is a smooth graph ⋮ Large-time behavior of solutions of parabolic equations on the real line with convergent initial data. II: Equal limits at infinity ⋮ The attractor of the scalar reaction diffusion equation is a smooth graph ⋮ Connectivity and design of planar global attractors of Sturm type. II: Connection graphs ⋮ Dynamics of bifurcations for variational problems with \(O(3)\) equivariance: A Conley index approach ⋮ A Lyapunov function for fully nonlinear parabolic equations in one spatial variable ⋮ A sequence of order relations: Encoding heteroclinic connections in scalar parabolic PDE ⋮ Sharp asymptotics of metastable transition times for one dimensional SPDEs ⋮ Sturm 3-ball global attractors. 1: Thom-Smale complexes and meanders ⋮ RECENT DEVELOPMENTS IN DYNAMICAL SYSTEMS: THREE PERSPECTIVES ⋮ Connectivity and design of planar global attractors of Sturm type. III: Small and platonic examples ⋮ Orbit equivalence of global attractors of semilinear parabolic differential equations ⋮ Sturm attractors for quasilinear parabolic equations with singular coefficients ⋮ Scalar parabolic PDEs and braids ⋮ Slowly non-dissipative equations with oscillating growth ⋮ Connectivity and design of planar global attractors of Sturm type, I: Bipolar orientations and Hamiltonian paths ⋮ Homoclinic and heteroclinic orbits for a semilinear parabolic equation ⋮ Sturm 3-ball global attractors 2: design of Thom-Smale complexes ⋮ Discrete Ljapunov functionals and $\omega $-limit sets ⋮ Superstable manifolds of semilinear parabolic problems ⋮ Numerical Continuation at Double Bifurcation Points of a Reaction–Diffusion Problem ⋮ Realization of meander permutations by boundary value problems ⋮ Limiting classification on linearized eigenvalue problems for 1-dimensional Allen-Cahn equation. I. Asymptotic formulas of eigenvalues ⋮ Boundary orders and geometry of the signed Thom-Smale complex for Sturm global attractors ⋮ Anisotropic Einstein data with isotropic non negative prescribed scalar curvature ⋮ A permutation related to non-compact global attractors for slowly non-dissipative systems
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- An introduction to infinite dimensional dynamical systems -- geometric theory. With an appendix by Krzysztof P. Rybakowski
- Generic properties of stationary state solutions of reaction-diffusion equations
- Some infinite-dimensional Morse-Smale systems defined by parabolic partial differential equations
- The Morse-Smale property for a semilinear parabolic equation
- Geometric theory of semilinear parabolic equations
- Generic bifurcation of steady-state solutions
- The Connection Matrix Theory for Morse Decompositions
- Numbers of zeros on invariant manifolds in reaction- diffusion equations
- Generic hyperbolicity in one-dimensional reaction- diffusion equations with general boundary conditions
This page was built for publication: Connecting orbits in scalar reaction diffusion equations. II: The complete solution