2 citations · 5 across the 14 of their papers we have counts for
14 papers
Pullback dynamics for a semilinear heat equation with homogeneous Neumann boundary conditions on time-varying domains
Gleiciane S. Aragão, Flank D. M. Bezerra, Lucas G. Mendonça
We are interested in studying a non-autonomous semilinear heat equation with homogeneous Neumann boundary conditions on time-varying domains. Using a differential geometry approach…
Upper semicontinuity for a class of nonlocal evolution equations with Neumann condition
Flank D. M. Bezerra, Silvia Sastre-Gomez, Severino H. da Silva
In this paper we consider the following nonlocal autonomous evolution equation in a bounded domain in \[ \partial_t u(x,t) =- h(x)u(x,t) + g \Big(\int_Ω J(x,y)u(…
Fractional powers approach of maximal accretive operators for a class of third order abstract Cauchy problems
Mohammed Benharrat, Flank D. M. Bezerra
In this paper we explore the theory of fractional powers of maximal accretive operators to obtain results of existence, regularity and behavior asymptotic of solutions for linear a…
An extended version of the Cayley-Hamilton-Ziebur Theorem
Flank D. M. Bezerra, Lucas A. Santos
The aim of this paper is to prove a Cayley-Hamilton-Ziebur Theorem for non-autonomous semilinear matrix differential equations. Moreover, we show the applicability of results like…
Euler-Rodrigues formula for three-dimensional rotation via fractional powers of matrices
Flank D. M. Bezerra, Lucas A. Santos
In this short paper, we review the Euler-Rodrigues formula for three-dimensional rotation via fractional powers of matrices. We derive the rotations by any angle through the spectr…
Fractional powers approach of operators for higher order abstract Cauchy problems
Flank D. M. Bezerra, Lucas A. Santos
In this paper we explore the theory of fractional powers of non-negative (and not necessarily self-adjoint) operators and its amazing relationship with the Chebyshev polynomials of…
Well-posedness for some third-order evolution differential equations: A semigroup approach
Flank D. M. Bezerra, Alexandre N. Carvalho, Lucas A. Santos
In this paper, we discuss the well-posedness of the Cauchy problem associated with the third-order evolution equation in time $$ u_{ttt} +A u + ηA^{\frac13} u_{tt} +ηA^{\frac23} u_…
Fractional oscillon equations; solvability and connection with classical oscillon equations
Flank D. M. Bezerra, Rodiak N. Figueroa-López, Marcelo J. D. Nascimento
In this paper we are concerned with the asymptotic behavior of nonautonomous fractional approximations of oscillon equation $$ u_{tt}-μ(t)Δu+ω(t)u_t=f(u),\ x\inΩ,\ t\in\mathbb{R},…
The effect of perturbations on the convergence of attractors for reaction-diffusion equations concerning variations of nonlinear boundary conditions
Flank D. M. Bezerra, Marcone C. Pereira, Leonardo Pires
This paper presents estimates of the convergence of asymptotic dynamics of reaction-diffusion equations with nonlinear boundary conditions. We show how the convergence of the globa…
Dynamics of thermoelastic plate system with terms concentrated in the boundary: the lower semicontinuity of the global attractors
Gleiciane S. Aragão, Flank D. M. Bezerra, Cládio O. P. Da Silva
In this paper we show the lower semicontinuity of the global attractors of autonomous thermoelastic plate systems with Neumann boundary conditions when some reaction terms are conc…
Continuity of the set equilibria of non-autonomous damped wave equations with terms concentrating on the boundary
Flank D. M. Bezerra, Gleiciane da Silva Aragão
In this paper we are interested in the behavior of the solutions of non-autonomous damped wave equations when some reaction terms are concentrated in a neighborhood of the boundary…
Pullback attractors for a class of non-autonomous thermoelastic plate systems
Flank D. M. Bezerra, Vera L. Carbone, Marcelo J. D. Nascimento +1
In this article we study the asymptotic behavior of solutions, in sense of global pullback attractors, of the evolution system $$ \begin{cases} u_{tt} +ηΔ^2 u+a(t)Δθ=f(t,u), & t>τ,…
Pullback attractor for a non local non-autonomous evolution equation in an unbounded domain
Flank D. M. Bezerra, Miriam da S. Pereira, Severino H. da Silva
In this work we consider the non local evolution equation with time-dependent terms which arises in models of phase separation in \[ \partial_t u=- u + g \left(β(J*u…
Asymptotic behavior for a class of non autonomous non local problems
Flank D. Bezerra, Severino H. da Silva, Antonio L. Pereira
In this paper we consider the non local non autonomous evolution problem \[ \begin{cases} \partial_t u =- u + g \left(β(t)(Ku) \right)\ \ \mbox{in}\ \ Ω,\\ u = 0\ \ \mbox{in}\ \ \m…