| 60/2005 |
Morse Decomposition of Semiflows on Fiber Bundles Mauro Patrão, Luiz A. B. San Martin We study the chain transitivity and Morse decompositions of discrete and continuous-time semiflows on fiber bundles with emphasis on (generalized) flag bundles. In this case an algebraic description of the chain transitive sets is given. Our approach consists in embedding the semiflow in a semigroup of continuous maps to take advantage of the good properties of the semigroup actions on the flag manifolds.  rp-2005-60.pdf |
| 59/2005 |
The Einstein-Hilbert Lagrangian Density in a 2-Dimensional Spacetime is an Exact Differential Roldão da Rocha Jr., Waldyr A. Rodrigues Jr. Recently Kiriushcheva and Kuzmin \cite{kiku} claimed to have shown that the Einstein-Hilbert Lagrangian \textit{density} cannot be written in any coordinate gauge as an exact differential in a $2$-dimensional spacetime. Since this is contrary to other statements on on the subject found in the literature, as e.g., by Deser and Jackiw \cite{deserjackiw} and Jackiw \cite{jackiw} it is necessary to do decide who has reason. This is done in this paper in a very simply way using the Clifford bundle formalism. rp-2005-59.pdf |
| 58/2005 |
Formas Diferenciais em Eletrodinâmica Igor Leite Freire rp-2005-58.pdf |
| 57/2005 |
A Classification of Automorphisms of Compact 3-Manifolds Leonardo Navarro Carvalho, Ulrich Oertel We classify isotopy classes of automorphisms (self-homeomorphisms) of 3-manifolds satisfying the Thurston Geometrization Conjecture. The classification is similar to the classification of automorphisms ofsurfaces developed by Nielsen and Thurston, except an automorphism of a reducible manifold must first be written as a suitable composition of two automorphisms, each of which fits into our classification.Given an automorphism, the goal is to show, loosely speaking, either that it is periodic, or that it can be decomposed on a surface invariant up to isotopy, or that it has a ``dynamically nice" representative, with invariant laminations that ``fill" the manifold. We consider automorphisms of irreducible and boundary-irreducible 3-manifolds as being already classified, though there are some exceptional manifolds for which the automorphisms are not understood.Thus the paper is particularly aimed at understanding automorphisms of reducible and/or boundary reducible 3-manifolds.Previously unknown phenomena are found even in the case of connected sums of $S^2\times S^1$'s. To deal with this case, we prove that a minimal genus Heegaard decomposition is unique up to isotopy, a result which apparently was previously unknown.Much remains to be understood about some of the automorphisms of the classification. rp-2005-57.pdf |
| 56/2005 |
The Many Faces of Maxwell, Dirac and Einstein Equations. A Clifford Bundle Approach Waldyr A. Rodrigues Jr., Edmundo Capelas de Oliveira First draft of a research book on Maxwell, Dirac and Einstein equations. |
| 55/2005 |
Error Estimates for Semi-Galerkin Approximations of Nonhomogeneous Incompressible Fluids P. Braz e Silva, Marko A. Rojas-Medar We consider the spectral semi-Galerkin method applied to the nonhomogeneous Navier-Stokes equations. Under certain conditions it is known that the approximate solutions constructed through this method converge to a global strong solution of these equations. Here, we derive an optimal uniform in time error estimate in the $H^1$ norm for the velocity. We also derive an error estimate for the density in some spaces $L^r$. rp-2005-55.pdf |
| 54/2005 |
The Heat Equation with Singular Nonlinearity and Singular Initial Data M. Loayza We study the existence, uniqueness and regularity of solutions of the parabolic equation $u_t -\Delta u = a(x)u^q + b(x)u^p$ in a bounded domain and with Dirichlet’s condition on the boundary. We consider here $a\in L^\alpha(\Omega)$; $b \in L^\beta(\Omega)$ and $0 < q \le 1 < p. The initial data $u(0) = u_0$ is considered in the space $L^r(\Omega)$, $r\ge 1$. In the main result $(0 < q < 1)$, we assumethat $a$, $b\ge 0$ a.e in $\Omega$ and we assume that $u_0\ge \gamma d_\Omega$ for some $\gamma > 0$. We find a unique solution $C([0; T];L^r(\Omega)) \cap L^\infty_{loc} ((0; T);L^\infty(\Omega))$. rp-2005-54.pdf |
| 53/2005 |
A Mathematical Analysis of an Optimal Control Problem for a Generalized Boussinesq Model for Viscous Incompressible Flows José Luiz Boldrini, E. Fernández-Cara, Marko A. Rojas-Medar We consider an optimal control problem governed by a systems of nonlinear partial differential equations modeling viscous incompressible flows submitted to variations of temperature, using a generalized Boussinesq approximation. We obtain existence for the optimal control as well as first order optimality conditions of Pontriagyn type by using the formalism due to Dubovitskii and Milyutin. rp-2005-53.pdf |
| 52/2005 |
Nonsmooth Continuous-time Optimization Problems via Invexity Adilson J. Vieira-Brandão, Valeriano A. de Oliveira, Marko A. Rojas-Medar We introduce the notion of KKT-invexity for nonsmooth continuous-time nonlinear optimization problems and prove that this notion is a necessary and sufficient condition for global optimality of a Karush-Kuhn-Tucker point. rp-2005-52.pdf |
| 51/2005 |
Vanishing Viscosity for Non-Homogeneous Asymmetric Fluids in R^3 P. Braz e Silva, E. Fernández-Cara, Marko A. Rojas-Medar We consider a non-homogeneous, viscous, incompressible asymmetric fluid in $R^3$. We prove that there exists a small time interval where the fluid variables converge uniformly as the viscosities tend to zero. In the limit, we find a non-homogeneous, non-viscous, incompressible asymmetric fluid governed by an Euler-like system. rp-2005-51.pdf |
