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Sturm Attractors for Quasilinear Parabolic Equations with Singular Coefficients

  • Phillipo LappicyEmail author
Article

Abstract

The goal of this paper is to construct explicitly the global attractors of parabolic equations with singular diffusion coefficients on the boundary, as it was done without the singular term for the semilinear case by Brunovský and Fiedler (1986), generalized by Fiedler and Rocha (1996) and later for quasilinear equations by Lappicy (2017). In particular, we construct heteroclinic connections between hyperbolic equilibria, stating necessary and sufficient conditions for heteroclinics to occur. Such conditions can be computed through a permutation of the equilibria. Lastly, an example is computed yielding the well known Chafee–Infante attractor.

Keywords

Parabolic equations Singular coefficients Infinite dimensional dynamical systems Global attractor Sturm attractor 

Notes

Acknowledgements

The author thank once again all who were previously acknowledged in his Phd thesis. Further he thank Je-Chiang Tsai for finding a mistake in the shooting curve construction, that has been fixed. Funding was provided by CAPES (Grant No. 99999.009627).

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Authors and Affiliations

  1. 1.Instituto de Ciências Matemáticas e de ComputaçãoUniversidade de São PauloSão CarlosBrazil

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