The Morse-Smale structure of a generic reaction-diffusion equation in higher space dimension
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Publication:678605
DOI10.1006/jdeq.1996.3234zbMath0868.35062OpenAlexW2044572865MaRDI QIDQ678605
Pavol Brunovský, Peter Poláčik
Publication date: 21 August 1997
Published in: Journal of Differential Equations (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1006/jdeq.1996.3234
Reaction-diffusion equations (35K57) Degenerate parabolic equations (35K65) Morse-Smale systems (37D15)
Related Items (32)
Generic hyperbolicity for the equilibria of the one-dimensional parabolic equation\newline \(u_t=(a(x)u_x)+f(u)\) ⋮ Semicontinuity of attractors for impulsive dynamical systems ⋮ Dissipation and compact attractors ⋮ Uniform exponential dichotomy and continuity of attractors for singularly perturbed damped wave equations ⋮ A class of generically Morse-Smale monotone, dynamical systems ⋮ Topological structural stability of partial differential equations on projected spaces ⋮ Continuity of non-autonomous attractors for hyperbolic perturbation of parabolic equations ⋮ Lipschitz perturbations of Morse-Smale semigroups ⋮ Sturm attractors for fully nonlinear parabolic equations ⋮ Generic Morse-Smale property for the parabolic equation on the circle ⋮ Global bifurcation in \(2m\)-order generic systems of nonlinear boundary value problems ⋮ Global attractors of generic reaction diffusion equations under Lipschitz perturbations ⋮ Convergence and asymptotic stabilization for some damped hyperbolic equations with non-isolated equilibria ⋮ The generic gradient-like structure of certain asymptotically autonomous semilinear parabolic equations ⋮ Dynamics of the viscous Cahn-Hilliard equation ⋮ Forward attraction of pullback attractors and synchronizing behavior of gradient-like systems with nonautonomous perturbations ⋮ Adaptation of the generic PDE's results to the notion of prevalence ⋮ Regularity of solutions on the global attractor for a semilinear damped wave equation ⋮ The gradient and heavy ball with friction dynamical systems: The quasiconvex case ⋮ Topological instabilities in families of semilinear parabolic problems subject to nonlinear perturbations ⋮ Generic hyperbolicity of stationary solutions for a reaction-diffusion system ⋮ Generic hyperbolicity of equilibria and periodic orbits of the parabolic equation on the circle ⋮ The Conley index along heteroclinic trajectories of reaction-diffusion equations ⋮ Equilibrium-like solutions of asymptotically autonomous differential equations ⋮ Superstable manifolds of semilinear parabolic problems ⋮ Generic transversality property for a class of wave equations with variable damping ⋮ Nonautonomous Conley index theory the connecting homomorphism ⋮ Persistent saddle connections in a class of reaction-diffusion equations ⋮ Generic transversality of heteroclinic and homoclinic orbits for scalar parabolic equations ⋮ Nonautonomous perturbations of Morse-Smale semigroups: stability of the phase diagram ⋮ On the Morse complex for semilinear parabolic equations ⋮ Nonconvergent bounded solutions of semilinear heat equations on arbitrary domains
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