Asymptotic Analysis - Volume 7, issue 3

Authors: Conrad, Francis | Rao, Bopeng

Article Type: Research Article

Abstract: We study the uniform stabilization of the wave equation by means of a nonlinear dissipative boundary feedback. We consider a Neumann condition on the whole boundary, and the observation is the boundary displacement and velocity. We obtain, in a nonlinear framework, estimates of the decay, for any displacement. We establish a similar result for the one-dimensional wave equation with a variable coefficient.

DOI: 10.3233/ASY-1993-7301

Citation: Asymptotic Analysis, vol. 7, no. 3, pp. 159-177, 1993

Authors: Gruais, Isabelle

Article Type: Research Article

Abstract: The asymptotic expansions method is used to study the limit behaviour of a system made of a plate of small thickness 2ε in which one partly inserted a rod of cross section equal to 4ε2 . When the free extremity of the rod is clamped and when the materials are nonlinearly elastic, it turns out that the transverse displacement of the rod around the junction is “almost” rigid. Moreover, the plate, which is somehow held by the rod, has a torsion equal to zero around the junction, which makes impossible any free rotation around the axis of the rod.

DOI: 10.3233/ASY-1993-7302

Citation: Asymptotic Analysis, vol. 7, no. 3, pp. 179-194, 1993

Authors: Sukhanov, V.V.

Article Type: Research Article

Abstract: A study is made of the asymptotic behaviour of the solutions of the nonlinear nonintegrable equations of KdV type. The formal solutions in three regions: x/t>0, x/t<0, x/t1/3 =O(1) are constructed. As a result of the the investigation of the rearrangement of those solutions formulas connecting the parameters of asymptotics in different regions are obtained. The final formula corresponds the relation connecting the amplitude of the solutions which is exponentially decreasing as x→−∞ and the amplitude of the solution of the dispersion type for the KdV equation. All constructions are carried out within the context of formal solutions.

DOI: 10.3233/ASY-1993-7303

Citation: Asymptotic Analysis, vol. 7, no. 3, pp. 195-205, 1993

Authors: Wang, Shixiao

Article Type: Research Article

Abstract: We study the behaviour of the solutions of a nonlinear elliptic equation. We show when there exists a uniform estimate for a sequence of solutions of this equation and when there does not exist such an estimate; in this case we provide a blow-up example.

DOI: 10.3233/ASY-1993-7304

Citation: Asymptotic Analysis, vol. 7, no. 3, pp. 207-213, 1993

Authors: Tabara, Tatsuhiko J.

Article Type: Research Article

Abstract: We will consider the following boundary value problem for a second-order linear differential equation with polynomial coefficients in the complex plane: is there a differential equation of the specific type with linearly independent solutions y1 (x) and y2 (x) such that the ratio y1 (x)/y2 (x) can be prescribed both at the origin and at infinity? We shall derive uniqueness conditions for the problem.

DOI: 10.3233/ASY-1993-7305

Citation: Asymptotic Analysis, vol. 7, no. 3, pp. 215-231, 1993