arXiv subjects

Phillipo Lappicy

Publications and source records attributed to Phillipo Lappicy.

21 records · Page 2Linked to original sources

arXiv2018

Space of initial data for self-similar Schwarzschild solutions

The Einstein constraint equations describe the space of initial data for the evolution equations, dictating how space should curve within spacetime. Under certain assumptions, the constraints reduce to a scalar quasilinear parabolic equation on the sphere with various singularities, and nonlinearity being the prescribed scalar curvature of space. We focus on self-similar Schwarzschild solutions. Those describe, for example, the initial data of black holes. We construct the space of initial data for such solutions, and show that the event horizon is related with global attractors of such parabolic equations. Lastly, some properties of those attractors and its solutions are explored.

gr-qc↗

arXiv2018

Sturm attractors for quasilinear parabolic equations with singular coefficients

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 Brunovsk'y and Fiedler (1986), generalized by Fiedler and Rocha (1996) and later for quasilinear equa- tions by the author (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.

math.DS↗

arXiv2018

Sturm attractors for quasilinear parabolic equations

The goal of this paper is to construct explicitly the global attractors of quasilinear parabolic equations, as it was done for the semilinear case by Brunovský and Fiedler (1986), and generalized by Fiedler and Rocha (1996). 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.

math.DS↗