Boundary Orders and Geometry of the Signed Thom–Smale Complex for Sturm Global Attractors

@article{Fiedler2018BoundaryOA,
  title={Boundary Orders and Geometry of the Signed Thom–Smale Complex for Sturm Global Attractors},
  author={B. Fiedler and C. Rocha},
  journal={Journal of Dynamics and Differential Equations},
  year={2018},
  pages={1-32}
}
  • B. Fiedler, C. Rocha
  • Published 2018
  • Mathematics
  • Journal of Dynamics and Differential Equations
  • We embark on a detailed analysis of the close relations between combinatorial and geometric aspects of the scalar parabolic PDE * $$\begin{aligned} u_t = u_{xx} + f(x,u,u_x) \end{aligned}$$ u t = u xx + f ( x , u , u x ) on the unit interval $$0< x<1$$ 0 < x < 1 with Neumann boundary conditions. We assume f to be dissipative with N hyperbolic equilibria $$v\in {\mathcal {E}}$$ v ∈ E . The global attractor $${\mathcal {A}}$$ A of (*), also called Sturm global attractor , consists of the unstable… CONTINUE READING

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    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 58 REFERENCES
    Geometric Theory of Semilinear Parabolic Equations
    • 4,878
    Asymptotic Behavior of Dissipative Systems
    • 2,212
    • Open Access
    Infinite-Dimensional Dynamical Systems in Mechanics and Physics (Roger Temam)
    • 1,691
    • Open Access
    Attractors of Evolution Equations
    • 1,088
    Attractors for semigroups and evolution equations
    • 542
    • Open Access
    Attractors for Equations of Mathematical Physics
    • 757
    • Open Access