Jáuber Cavalcante de Oliveira
Recent Publications
Time-periodic flows of magnetic fluids,
Partial Differential Equations and Applications 3, 18 (2022).
Abstract: We prove the existence T -periodic weak and strong solutions for the system of partial differ- ential equations corresponding to the three-dimensional Shliomis model for magnetic fluids in bounded domains subjected to T -periodic external magnetic field. For the existence of strong solution we assume that the external magnetic field is sufficiently small.
Strong
Solutions for Ferrofluid Equations in Exterior Domains,
Acta Applicandae
Mathematicae 156: 1-14, (2018)
Abstract: We prove the global existence strong solutions for the system of partial differential equations corresponding to the Shliomis model for magnetic fluids in exterior domains without regularization terms in the magnetization equation under the assumption of small data and also small coupling parameter.
Asymptotic
Behavior of Solutions for the Magneto-thermo-elastic System in R^3
(with C. R. da Luz)
Journal
of Mathematical Analysis and Applications,
432
(2015), 1200-1215.
Abstract: We investigate the asymptotic behavior of solutions for the Cauchy problem described by a system of magneto-thermo-elastic equations. We obtain improved decay rates with less demands on the initial data when compared to previous results in the literature.
Long
time dynamics of a multidimensional nonlinear lattice with memory
(with J. M. Pereira and G. P. Menzala)
Discrete
and Continuous Dynamical Systems,
Series B, 20
(8)
2015, 2715–2732.
Abstract: This work is devoted to study the nature of vibrations arising in a multidimensional nonlinear periodic lattice structure with memory. We prove the existence of a global attractor. In the homogeneous case under a restriction on the nonlinear term we obtain decay rates of the total energy. These rates could be exponential, polynomial or several other intermediate types.
Asymptotic
stability and regularity of solutions for a magnetoelastic system in
bounded domains,
Acta
Mathematica Vietnamica,
39(2)
(2014), 133-150.
Abstract: We prove the existence of strong time-periodic solutions and their asymptotic stability with the total energy of the perturbations decaying to zero at an exponential decay rate as t goes to infinity for a semilinear (nonlinearly coupled) magnetoelastic system in bounded, simply connected, three-dimensional domain. The mathematical model includes a mechanical dissipation and a periodic forcing function of period T. In the second part of the paper, we consider a magnetoelastic system in the form of a semilinear initial boundary value problem in a bounded, simply-connected two-dimensional domain. We use LaSalle invariance principle to obtain results on the asymptotic behavior of solutions. This second result was obtained for the system under the action of only one dissipation (the natural dissipation of the system).
Existence
of time-periodic solutions for a magnetoelastic system in bounded
domains (with
M. Mohebbi)
Journal
of Elasticity 113
(2013), pp. 113-133.
Abstract: We investigate the existence of periodic solutions for a semilinear (nonlinearly coupled) magnetoelastic system in bounded, simply connected, three-dimensional domains with boundaries of class $C^2$. The mathematical model includes a nonlinear mechanical dissipation like $\rho(u^{'})=|u^{'}|^{p}u^{'}$ and a periodic forcing function of period $T$. We prove the existence of $T$-periodic weak solutions when $p \in [3,4]$ (p=0 being a simpler case). In the corresponding two-dimensional case, the existence result holds under the assumption that $p \geq 2$.
Decay
rates of magnetoelastic waves in an unbounded conductive medium
(with R.C. Charão, G.P.
Menzala)
Eletronic
Journal of Differential Equations 2011,
No. 127, 14pp.
Abstract: We study the uniform decay of the total energy of solutions for a system in magnetoelasticity with localized damping near infinity in an exterior 3-D domain. Using appropriate multipliers and recent work by Charao and Ikekata [3], we conclude that the energy decays at the same rate as (1+t)^{-1} when t -> infinity.
Global
attractor for a class of nonlinear lattices (with
J.M. Pereira)
Journal of Mathematical Analysis and Applications .
370 (2010), No. 2, 726-739.
Abstract: We consider a class of
nonlinear lattices with nonlinear damping
$\ddot u_n(t)+(-1)^p \Delta^p u_n(t)+\alpha u_n(t)+h(u_n(t))+ g(n,\dot u_n(t))=f_n$
where $N \in Z$, $t \in R^{+}$ is a real positive constant, p is any positive integer and $\Delta$ is the discrete one-dimensional Laplace operator. Under suitable conditions on $h$ and $g$ we prove the existence of a global attractor for the continuous semigroup associated with the above equation.
Our proofs are based on a difference inequality due to M. Nakao [M. Nakao, Global attractors for nonlinear wave equations with nonlinear dissipative terms, J. Differential Equations 227 (2006) 204–229].
Large
time behavior of multidimensional nonlinear lattices with nonlinear
damping (wih
J.M. Pereira, G.P. Menzala)
Communications
in Applied Analysis.
14 (2010), No. 2, 155-176.
Abstract: In this paper we study the asymptotic behavior of solutions of multidimensional nonlinear lattices subject to cyclic boundary conditions under the effect of a nonlinear dissipation. We establish the existence of a global attractor.
Energy
decay rates of magnetoelastic waves in a bounded conductive medium
(with R.C. Charão, G.P.
Menzala)
Discrete
and Continuous Dynamical Systems-A 25
(2009), No. 3, 797-821.
Abstract: We consider a coupled system of evolution equations modeling the propagation of elastic waves interacting with a magnetic field in a bounded simply connected region of $R^3$ with boundary of class $C^2$ A nonlinear dissipative mechanism is allowed to be effective in an small subregion of $\Omega$. We prove that the total energy decays as t tends to infinity .
Address:
Departamento de Matemática,
Universidade Federal de Santa
Catarina,
CEP 88040-900 Florianópolis, SC
Brasil
E-mails: j.c.oliveira@ufsc.br, jauber.coliveira@gmail.com
phone: (+55)(48) 37213693