Asymptotic expansion of the heat kernel for a class of hypoelliptic operators
Asymptotic expansions for bounded solutions to semilinear Fuchsian equations.
Asymptotic expansions for linear symmetric hyperbolic systems with small parameter.
Asymptotic Expansions for the Solutions of Certain Nonlinear Parabolic Problems. I .
Asymptotic expansions of quasiperiodic solutions
Asymptotic integration of parabolic problems with large high-frequency summands.
Asymptotic models for scattering from unbounded media with high conductivity
We analyze the accuracy and well-posedness of generalized impedance boundary value problems in the framework of scattering problems from unbounded highly absorbing media. We restrict ourselves in this first work to the scalar problem (E-mode for electromagnetic scattering problems). Compared to earlier works, the unboundedness of the rough absorbing layer introduces severe difficulties in the analysis for the generalized impedance boundary conditions, since classical compactness arguments are no...
Asymptotic representation of solutions to the Dirichlet problem for elliptic systems with discontinuous coefficients near the boundary.
Asymptotic representations for solutions of bisingular problems.
Asymptotic solutions of equations with slowly varying coefficients
Asymptotic theory for weakly nonlinear wave equations in semi-infinite domains.
Asymptotics for multifractal conservation laws
We study asymptotic behavior of solutions to multifractal Burgers-type equation , where the operator A is a linear combination of fractional powers of the second derivative and f is a polynomial nonlinearity. Such equations appear in continuum mechanics as models with fractal diffusion. The results include decay rates of the -norms, 1 ≤ p ≤ ∞, of solutions as time tends to infinity, as well as determination of two successive terms of the asymptotic expansion of solutions.
Asymptotics of solutions to Stokes and Navier-Stokes equations in domains with paraboloidal outlets to infinity
Asymptotics of solutions to the Dirichlet-Cauchy problem for parabolic equations in domains with edges
This paper is concerned with the Dirichlet-Cauchy problem for second order parabolic equations in domains with edges. The asymptotic behaviour of the solution near the edge is studied.
Asymptotique des pôles de la matrice de scattering pour deux obstacles strictement convexes
Behaviour of the first eigenvalue of the p-Laplacian in a domain with a hole
We investigate the behaviour of a sequence , s = 1,2,..., of eigenvalues of the Dirichlet problem for the p-Laplacian in the domains , s = 1,2,..., obtained by removing from a given domain Ω a set whose diameter vanishes when s → ∞. We estimate the deviation of from the eigenvalue of the limit problem. For the derivation of our results we construct an appropriate asymptotic expansion for the sequence of solutions of the original eigenvalue problem.
Borel summable solutions of the Burgers equation
We give necessary and sufficient conditions for the formal power series solutions to the initial value problem for the Burgers equation to be convergent or Borel summable.
Boundary layer correctors and generalized polarization tensor for periodic rough thin layers. A review for the conductivity problem
We study the behaviour of the steady-state voltage potential in a material composed of a two-dimensional object surrounded by a rough thin layer and embedded in an ambient medium. The roughness of the layer is supposed to be εα–periodic, ε being the magnitude of the mean thickness of the layer, and α a positive parameter describing the degree of roughness. For ε tending to zero, we determine the appropriate boundary layer correctors which lead to approximate transmission conditions equivalent to...
Boundary layer for Chaffee-Infante type equation
This article is concerned with the nonlinear singular perturbation problem due to small diffusivity in nonlinear evolution equations of Chaffee-Infante type. The boundary layer appearing at the boundary of the domain is fully described by a corrector which is “explicitly" constructed. This corrector allows us to obtain convergence in Sobolev spaces up to the boundary.
Boundary layers and glancing blow-up in nonlinear geometric optics