Asymptotic Analysis - Volume 66, issue 2

Authors: Montefusco, Eugenio | Pellacci, Benedetta | Squassina, Marco

Article Type: Research Article

Abstract: The semiclassical limit of a weakly coupled nonlinear focusing Schrödinger system in presence of a nonconstant potential is studied. The initial data is of the form (u1 , u2 ) with ui =ri ((x−x˜)/ε)e(i/ε)x·ξ˜ , where (r1 , r2 ) is a real ground state solution, belonging to a suitable class, of an associated autonomous elliptic system. For ε sufficiently small, the solution (ϕ1 , ϕ2 ) will been shown to have, locally in time, the form (r1 ((x−x(t))/ε)e(i/ε)x·ξ(t) , r2 ((x−x(t))/ε)e(i/ε)x·ξ(t) ), where (x(t), ξ(t)) is the solution of the Hamiltonian system x˙(t)=ξ(t), ξ˙(t)=−∇V(x(t)) with x(0)=x˜ …and ξ(0)=ξ˜. Show more

Keywords: weakly coupled nonlinear Schrödinger systems, concentration phenomena, semiclassical limit, orbital stability of ground states, soliton dynamics

DOI: 10.3233/ASY-2009-0959

Citation: Asymptotic Analysis, vol. 66, no. 2, pp. 61-86, 2010

Authors: Pompe, Waldemar

Article Type: Research Article

Abstract: We prove existence of a solution to the nonautonomous, noncoercive, quasistatic models in the viscoplasticity theory. This extends the results shown earlier by the author in Math. Methods Appl. Sci. 27 (2004), 1347–1365 and Math. Methods Appl. Sci. 31 (2008), 775–792, for the autonomous case. As a special case we obtain existence of the solution to the nonautonomous kinematic hardening model, where the constitutive nonlinearity has a polynomial or a rapid growth at infinity.

Keywords: viscoplasticity models, Orlicz spaces, semigroups of contractions

DOI: 10.3233/ASY-2009-0960

Citation: Asymptotic Analysis, vol. 66, no. 2, pp. 87-102, 2010

Authors: Alfaro, Manuel | Peña, Ana | Rezola, M. Luisa | Moreno-Balcázar, Juan José

Article Type: Research Article

Abstract: We consider a generalization of the classical Hermite polynomials by the addition of terms involving derivatives in the inner product. This type of generalization has been studied in the literature from the point of view of the algebraic properties. Thus, our aim is to study the asymptotics of this sequence of nonstandard orthogonal polynomials. In fact, we obtain Mehler–Heine type formulas for these polynomials and, as a consequence, we prove that there exists an acceleration of the convergence of the smallest positive zeros of these generalized Hermite polynomials towards the origin.

Keywords: asymptotics, Hermite polynomials, Mehler–Heine type formulas, zeros, Bessel functions

DOI: 10.3233/ASY-2009-0961

Citation: Asymptotic Analysis, vol. 66, no. 2, pp. 103-117, 2010

Authors: Vasconcellos, Carlos F. | da Silva, Patricia N.

Article Type: Correction

Abstract: In this erratum of the article: “Stabilization of the linear Kawahara equation with localized damping”, published in Asymptotic Analysis 58(4) (2008), 229–252, DOI 10.3233ASY-2008-0895, we shall fix a mistake which was done when we proved the existence and we defined the countable set of the lengths L where the decay of the energy fails, a set named 𝒩, see Lemma 2.1, p. 235. We considered the equation defined by λu0 +u0 ‴+u0 '''''=0, which is wrong since the parameter η in the Kawahara equation was completely forgotten and it makes changing in the result. In fact, η is a negative …constant and the correct equation is λu0 +u0 ‴+ηu0 '''''=0. Then, as η<0 we can prove, in this case, that the set 𝒩 is empty. Therefore, we obtain that the energy associated with linear Kawahara equation decays exponentially for all lengths L, even in absence of the damping. In the new proof for Lemma 2.1, remain the same idea and the same arguments of the original proof, but the signal of parameter η produces different final result. Show more

DOI: 10.3233/ASY-2010-0987

Citation: Asymptotic Analysis, vol. 66, no. 2, pp. 119-124, 2010