Connectivity and Design of Planar Global Attractors of Sturm Type . I : Bipolar Orientations and Hamiltonian Paths

Abstract

Based on a Morse-Smale structure we study planar global attractors Af of the scalar reaction-advection-diffusion equation ut = uxx + f(x, u, ux) in one space dimension. We assume Neumann boundary conditions on the unit interval, dissipativeness of f , and hyperbolicity of equilibria. We call Af Sturm attractor because our results strongly rely on nonlinear… (More)

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