Asymptotic behavior of <i>u</i>-capacities and singular perturbations for the Dirichlet-Laplacian

Singular Asymptotic Expansions for Dirichlet Eigenvalues and Eigenfunctions of the Laplacian on Thin Planar Domains

We consider the Laplace operator with Dirichlet boundary conditions on a planar domain and study the effect that performing a scaling in one direction has on the spectrum. We derive the asymptotic expansion for the eigenvalues and corresponding eigenfunctions as a function of the scaling parameter around zero. This method allows us, for instance, to obtain an approximation for the first Dirichl...

On the Asymptotic Behavior of Elliptic, Anisotropic Singular Perturbations Problems

In this paper, we consider anitropic singular perturbations of some elliptic boundary value problems. We study the asymptotic behavior as ε → 0 for the solution. Strong convergence in some Sobolev spaces is proved and the rate of convergence in cylindrical domains is given.

Singular Dirichlet Problem for Ordinary Differential Equations with Φ-laplacian

We provide sufficient conditions for solvability of a singular Dirichlet boundary value problem with φ-Laplacian (φ(u)) = f(t, u, u), u(0) = A, u(T ) = B, where φ is an increasing homeomorphism, φ( ) = , φ(0) = 0, f satisfies the Carathéodory conditions on each set [a, b] × 2 with [a, b] ⊂ (0, T ) and f is not integrable on [0, T ] for some fixed values of its phase variables. We prove the exis...

Topics in Singular Perturbations and Hybrid Asymptotic-Numerical Methods

Hybrid asymptotic-numerical methods are used to study various singular perturbation problems where innnite logarithmic asymptotic expansions occur. In particular, they are used to sum the innnite logarithmic expansions that arise for a low Reynolds number ow problem and for certain two-dimensional eigenvalue problems in perforated domains. Asymptotic and numerical methods are also used to analy...

Asymptotic Behavior of Solution for p-Laplacian Type Wave Equation