# Carlos Frederico Vasconcellos's research while affiliated with Instituto Nacional de Matemática Pura e Aplicada and other places

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## Publications (13)

In this study, we characterize the lengths of intervals for
which the linear Kawahara equation has a non-trivial solution,
whose energy is stationary. This gives rise to a family of complex
functions. Characterizing the lengths amounts to deciding which members
of this family are entire functions. Our approach is essentially
based on determining th...

A selecao de carteiras de investimentos e considerada um dos principais problemas em financas e esta diretamente relacionada a Teoria Moderna de Portfolio, que envolve conceitos fundamentais como risco de ativos, retorno esperado de investimentos, correlacao entre ativos e diversificacao, que podem ser descritos atraves de conceitos da probabilidad...

We analyze the stabilization and internal exact control for the Kuramoto-Sivashinsky equation (KS) in a bounded interval. That is, we consider the following equation: u t +αu xx +βu xxx +ηu xxxx +uu x =0· The above equation is a model for small amplitude long waves. Using multiplier techniques we prove the exponential decay of the total energy asso...

We analyze the stabilization and the exact controllability of a third order linear equation in a bounded interval. That is, we consider the following equation: iut+iγux+αuxx+iβuxxx where u = u(x; t) is a complex valued function defined in (0; L) × (0;+∞) and α, β and γ are real constants. Using multiplier techniques, HUM method and a special unifor...

We study the stabilization of global solutions of the linear Kawahara (K) equation in a bounded interval under the effect of a localized damping mechanism. The Kawahara equation is a model for small amplitude long waves. Using multiplier techniques and compactness arguments we prove the exponential decay of the solutions of the (K) model. We also p...

We study the stabilization of global solutions of the
Kawahara (K) equation in a bounded interval, under the effect of
a localized damping mechanism. The Kawahara equation is a model
for small amplitude long waves. Using multiplier techniques and
compactness arguments we prove the
exponential decay of the solutions of the (K) model. The proof
requi...

## Citations

... Faremos uma caracterização completa dos sistemas incluindo os casos degenerados que não foram tratados por Athayde e Flôres [1]. Avançamos assim na análise matemática do modelo de Athayde e Flôres [1] feita em Martins, Vasconcellos e Silva [4][5][6] ao atacar questões deixadas em aberto. Concentramo-nos agora na discussão sobre a dualidade a partir dos sistemas lineares associados aos multiplicadores dos problemas condicionados de minimização da variância e o seu dual, de maximização da assimetria. ...

... However, due to the complexity of the system, after taking the Fourier transform of the extended solution u, it is not possible to use the same techniques used in [30]. Thus, to prove our main result we invoke the result due Santos et al. [19]. Specifically, after taking the Fourier transform, the issue is to establish when a certain quotient of entire functions still turns out to be an entire function. ...

... Precisely, stabilization and control problems have been studied in recent years. A pioneer work is due to Silva and Vasconcellos [19]. The authors studied the stabilization of global solutions of the linear Kawahara equation in a bounded interval under the effect of a localized damping mechanism. ...

... then the L 2 −norm of the solution does not necessarily decay to zero. Here N is the set of critical lengths in the context of exact boundary controllability for the HLS (see [10,14] for the derivation of this set of critical lengths). For instance choosing the coefficients β = 1, α = 2 and δ = 8 with k = 1 and l = 2, we obtain L = π ∈ N . ...

... Then, the solution to a mixed problem for the KdV equation is obtained as a singular limit (b → 0) of solutions to the KdV-KS equation and the long-time behavior of the solutions is investigated for the KdV-KS equation and its limit case b → 0. It turned out that these outcomes can be extended to two coupled generalized KS equations [57,58]. Let us mention that the KS equation with a restrictive condition b 2 < 0 has been studied in [30,87], where it is shown that the solutions of the KS system are exponentially stable. This result is obtained in a more general nonlinear term in [81], whereas four different nonlinear adaptive control laws are designed in [26] so that solutions to the modified KS equation, with a higher order nonlinear term, are globally exponentially stable depending whether the parameters of the equation are known or unknown. ...

... More precisely, considering the damping localized at a subset ω ⊂ (0, L) containing nonempty neighborhoods of the end-points of an interval, it was shown that solutions of both linear and nonlinear problems for the KdV equation decay, independently on L > 0. In [34] it was proved that the same holds without cumbersome restrictions on ω ⊂ (0, L). In [42,44] the damping like in (1.8) was used for (1.7) without the drift term u x . If, however, the linear term u x is dropped, both the KdV and Kawahara equations do not possess critical set restrictions [36,43], and the damping is not necessary. ...

... • We point out that considering a = 0 in (1.2), Theorem 1.1 holds true. Additionally, no restriction is necessary in the length L > 0, and also Theorem 1.2 is still verified (see, for instance, [5,34] 7) on the length L. This is due to the choice of the Morawetz multipliers x in the expression of V 1 defined by (3.1). Therefore, the following natural question arises. ...