Publicações

2017
de Araujo ALA, de Magalhães PMD. On explicit L(QT)-estimates for a model of tissue invasion by solid tumors. Mathematical Methods in the Applied Sciences. 2017;40(13):4802-4811.Abstract
In this paper, we prove that if the initial data is small enough, we obtain an explicit L(QT)-estimate for a two-dimensional mathematical model of cancer invasion, proving an explicit bound with respect to time T for the estimate of solutions.
Coayla-Teran EA, de Magalhães PMD, Ferreira J. Existence of optimal controls for SPDE with locally monotone coefficientes. arxiv.org [Internet]. 2017;(arXiv:1704.04077). Publisher's VersionAbstract
The aim of this paper is to investigate the existence of optimal controls for systems described by stochastic partial differential equations (SPDEs) with locally monotone coefficients controlled by different external forces which are feedback controls. We apply our result to various types of SPDEs such as the stochastic 2-D Navier-Stokes equation, the stochastic nonlocal equation, stochastic linear equations and stochastic semilinear equations.
2015
de Anderson L.A. de Araujo PMMD. Existence of solutions and optimal control for a model of tissue invasion by solid tumors. Journal of Mathematical Analysis and Applications . 2015;421(2015):842-877.Abstract
In this paper we study the distributed optimal control problem for the two-dimensional mathematical model of cancer invasion. Existence of optimal state-control and stability is proved and an optimality system is derived.
2014
E.A.Coayla-Teran, J.Ferreira PMDde MHBde O. On a Stochastic Coupled System of Reaction-Diffusion of Nonlocal Type. In: From Particle Systems to Partial Differential Equations. Vol. 75. From Particle Systems to Partial Differential Equations. Springer-Verlag; 2014. pp. 301-320.Abstract
In this article we investigate the existence and uniqueness of weak solutions for a stochastic nonlinear parabolic coupled system of reaction-diffusion of nonlocal type, and with multiplicative white noise. An important result on the asymptotic behavior of the weak solutions is presented as well.
2012
E.A.Coayla-Teran, J.Ferreira PMDde MHBde O. On Stochastic Coupled System of Reaction-Diffusion of Nonlocal Type. Particle Systems and Partial Differential Equations I. 2012.Abstract
In this article we investigate the existence and uniqueness of weak solutions for a stochastic nonlinear parabolic coupled system of reaction-diffusion of nonlocal type, and with multiplicative white noise. An important result on the asymptotic behavior of the weak solutions is presented as well.
2008
Coayla-Teran EA, Ferreira J, de Magalhães PMD. Weak solutions for random nonlinear parabolic equations of nonlocal type. Random Operators/Stochastic Equations. 2008;16:213-222.Abstract
The existence and uniqueness of weak solutions for a random version of a class ofnonlinear parabolic problems of nonlocal type with additive noise are studied.
Adilson J.V. Brandão, Enrique Fernández-Cara PMDMMAR-M. Theoretical analysis and control results for the FitzHugh-Nagumo equation. Eletronic Journal of Differential Equations. 2008;2008(164):1-20.Abstract
In this paper we are concerned with some theoretical questions forthe FitzHugh-Nagumo equation. First, we recall the system, we briefly explain the meaning of the variables and we present a simple proof of the existence and uniqueness of strong solution. We also consider an optimal control problem for this system. In this context, the goal is to determine how can we act on the system in order to get good properties. We prove the existence of optimal state-control pairs and, as an application of the Dubovitski-Milyoutin formalism, we deduce the corresponding optimality system. We also connect the optimal control problem with a controllability question and we construct a sequence of controls that produce solutions that converge strongly to desired states. This provides a strategy to make the system behave as desired. Finally, we present some open questions related to the control of this equation.
2007
Coayla-Terán, Edson Alberto & Magalhães PMD. Stochastic FitzHugh-Nagumo Equations in a Time Dependent Domain. Random Operators and Stochastic Equations. 2007;15(1):49-64.Abstract
This article studies the existence of weak solutions for a stochastic version of the FitzHugh-Nagumo equations in a time dependent domain Q, where Q is a image of a cylinder C of Rn.
2003
P. M. Dias de Magalhães C-TEA. Weak Solutions for Stochastic FitzHugh-Nagumo Equations. Stochastic Analysis and Applications. 2003;21(2):443-463.Abstract
This article studies the existence of weak solutions for a stochastic version of the FtzHugh-Nagumo equations. The random elements are introduced through initial values and forcing terms of associated Cauchy problem, which may be white noise in the time. Moreover there is a dependence of a stochastic  parameter.
1999
de Magalhães PMD. A Mathematical Model for Freud's "Project". Revista da Pesquisa & Pós-Graduação. 1999;1(1):33-37.Abstract
Apresentamos um modelo matemático para a metapsicologia proposta por Freud em seu trabalho conhecido como o Projeto para uma Psicologia Científica . O modelo é consequência de uma associação entre os três arquétipos da Física-Matemática e os três sistemas neurais propostos por Freud.
1997
Magalhães DPM. Regularity for a Nonlinear Systems of Klein-Gordon Equations with Critical Nonlinearities. Bollettino U.M.I. 1997;7(11-B):587-604.Abstract
Si presenta un risultato di regolarità per un sistema non lineare di equazioni di Klein-Gordon con esponenti di Sobolev critici.