Connectivity and design of planar global attractors of Sturm type. II: Connection graphs
نویسندگان
چکیده
منابع مشابه
Connectivity and Design of Planar Global Attractors of Sturm Type. I: Bipolar Orientations and Hamiltonian Paths
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 nodal properties of Sturm type. The pl...
متن کاملConnectivity and Design of Planar Global Attractors of Sturm Type. III: Small and Platonic Examples
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 nodal properties of Sturm type. Plana...
متن کاملA permutation characterization of Sturm global attractors of Hamiltonian type
We consider Neumann boundary value problems of the form ut = uxx + f on the interval 0 ≤ x ≤ π for dissipative nonlinearities f = f(u). A permutation characterization for the global attractors of the semiflows generated by these equations is well known, even in the much more general case f = f(x, u, ux). We present a permutation characterization for the global attractors in the restrictive clas...
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چکیده ندارد.
Sturm 3-ball global attractors 3: Examples
1 Examples complete our trilogy on the geometric and combinatorial characterization of global Sturm attractors A which consist of a single closed 3-ball. The underlying scalar PDE is parabolic, ut = uxx + f(x, u, ux) , on the unit interval 0 < x < 1 with Neumann boundary conditions. Equilibria 2 vt = 0 are assumed to be hyperbolic. 3 4 Geometrically, we study the resulting Thom-Smale dynamic co...
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ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 2008
ISSN: 0022-0396
DOI: 10.1016/j.jde.2007.09.015