Asymptotic Analysis - Volume 56, issue 3-4

Authors: Houot, Jean | Munnier, Alexandre

Article Type: Research Article

Abstract: In this paper we study a coupled system of partial differential equations and ordinary differential equations. This system is a model for the 3d interactive free motion of rigid bodies immersed in an ideal fluid. Applying the least action principle of Lagrangian mechanics we prove that the degrees of freedom of the solids solve a system of second-order nonlinear ordinary differential equations. Under suitable smoothness assumptions on the fluid's domain boundary we prove the existence and C∞ regularity of the solids motion, up to a collision between two solids or between a solid with the boundary of the fluid's …domain. The case of an infinite cylinder surrounded by a fluid in a half space cavity is tackled. By a careful asymptotic analysis of a Neumann boundary value problem (solved by the fluid's potential) when the distance between the cylinder and the wall goes to zero we prove that collisions with non zero relative velocity can occur. Show more

Keywords: fluid–solid interaction, ideal fluid, Lagrangian mechanics, collisions, PDE–ODE coupled system

Citation: Asymptotic Analysis, vol. 56, no. 3-4, pp. 125-158, 2008

Authors: Nazarov, S.A. | Sokolowski, J.

Article Type: Research Article

Abstract: In the paper asymptotic analysis of spectral problems is performed for singular perturbations of geometrical domains. Asymptotic approximations of eigenvalues and eigenfunctions are constructed for the scalar, second-order boundary value problems. The presented results are constructive and can be used in the analysis of shape optimisation and inverse problems.

Keywords: singular perturbations, spectral problem, asymptotics of eigenfunctions and eigenvalues

Citation: Asymptotic Analysis, vol. 56, no. 3-4, pp. 159-204, 2008

Authors: Pallard, Christophe

Article Type: Research Article

Abstract: We show that the time of existence of classical solutions to the relativistic Vlasov–Maxwell system generated by fixed initial data tends to infinity as the speed of light becomes infinite.

Keywords: Vlasov–Maxwell system, Vlasov–Poisson system

Citation: Asymptotic Analysis, vol. 56, no. 3-4, pp. 205-228, 2008

Authors: Grasselli, Maurizio

Article Type: Research Article

Abstract: We consider a nonconserved phase-field model of Caginalp type which has been proposed by H.G. Rotstein et al. This model consists of two coupled integro-partial differential equations, one for the temperature ϑ, the other for the order parameter χ, and each one is characterized by a nonnegative decreasing memory kernel. Such equations, endowed with homogeneous Dirichlet (for ϑ) and Neumann (for χ) boundary conditions, generate a dissipative dynamical system which possesses a global attractor 𝒜. This fact was proven by V. Pata and the author. Here we construct a compact exponentially attracting set which, in particular, entails a smoothness result …for 𝒜. Then we also demonstrate the convergence of any trajectory to a single equilibrium, via the Łojasiewicz–Simon approach. Show more

Keywords: phase-field models, memory kernels, global attractors, convergence to equilibria

Citation: Asymptotic Analysis, vol. 56, no. 3-4, pp. 229-249, 2008

Article Type: Other

Citation: Asymptotic Analysis, vol. 56, no. 3-4, pp. 251-251, 2008