Ademir Fernando Pazoto

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Abstract. This work is devoted to prove the exponential decay for the energy of solutions of the Korteweg-de Vries equation in a bounded interval with a localized damping term. Following the method in Menzala (2002) which combines energy estimates, multipliers and compactness arguments the problem is reduced to prove the unique continuation of weak(More)
Abstract. This paper is concerned with the the asymptotic behavior of solutions of the critical generalized Korteweg-de Vries equation in a bounded interval with a localized damping term. Combining multiplier techniques and compactness arguments it is shown that the problem of exponential decay of the energy is reduced to prove the unique continuation(More)
A family of Boussinesq systems has recently been proposed by Bona, Chen, and Saut in [J.L. Bona, M. Chen, J.-C. Saut, Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media. I. Derivation and linear theory, J. Nonlinear Sci. 12 (4) (2002) 283–318] to describe the two-way propagation of small-amplitude gravity(More)
We study the semilinear nonlocal equation ut = J∗u− u− u in the whole R . First, we prove the global well-posedness for initial conditions u(x, 0) = u0(x) ∈ L(R ) ∩ L∞(RN ). Next, we obtain the long time behavior of the solutions. We show that different behaviours are possible depending on the exponent p and the kernel J : finite time extinction for p < 1,(More)
We consider a dynamical one-dimensional nonlinear von Kármán model for beams depending on a parameter ε > 0 and study its asymptotic behavior for t large, as ε → 0. Introducing appropriate damping mechanisms we show that the energy of solutions of the corresponding damped models decay exponentially uniformly with respect to the parameter ε. In order for(More)
In this work, we consider a class of linear dissipative evolution equations. We show that the solution of this class has a polynomial rate of decay as time tends to infinity, but does not have exponential decay. c © 2004 Elsevier Science Ltd. All rights reserved. Keywords—Dissipative systems, Decay rate, Semigroups.
In this paper, we study the boundary controllability of the Gear–Grimshaw system posed on a finite domain (0, L), with Neumann boundary conditions: ⎧ ⎪⎪⎪⎪⎨ ⎪⎪⎪⎪⎩ ut + uux + uxxx + avxxx + a1vvx + a2(uv)x = 0, in (0, L)× (0, T ), cvt + rvx + vvx + abuxxx + vxxx + a2buux + a1b(uv)x = 0, in (0, L)× (0, T ), uxx(0, t) = h0(t), ux(L, t) = h1(t), uxx(L, t) =(More)
Studied here is the large-time behavior of solutions of the Korteweg-de Vries equation posed on the right half-line under the effect of a localized damping. Assuming as in [20] that the damping is active on a set (a0,+∞) with a0 > 0, we establish the exponential decay of the solutions in the weighted spaces L((x + 1)dx) for m ∈ N∗ and L(edx) for b > 0 by a(More)