We establish an asymptotic representation formula for the steady state voltage perturbations caused by low volume fraction internal conductivity inhomogeneities. This formula generalizes and unifies earlier formulas derived for special geometries and distributions of inhomogeneities.
The main purpose of this article is to give a generalization of the logarithmic-type estimate in the Hardy-Sobolev spaces ; , and is the open unit disk or the annulus of the complex space .
This paper is concerned with the study of a model case of first order Hamilton-Jacobi equations posed on a “junction”, that is to say the union of a finite number of half-lines with a unique common point. The main result is a comparison principle. We also prove existence and stability of solutions. The two challenging difficulties are the singular geometry of the domain and the discontinuity of the Hamiltonian. As far as discontinuous Hamiltonians are concerned, these results seem to be new. They...
This is the first in a series of papers where we intend to show, in several steps, the existence of classical (or as classical as possible) solutions to a general two-phase free-boundary system. We plan to do so by:(a) constructing rather weak generalized solutions of the free-boundary problems,(b) showing that the free boundary of such solutions have nice measure theoretical properties (i.e., finite (n-1)-dimensional Hausdorff measure and the associated differentiability properties),(c) showing...
This paper examines a linear extrapolation time-discretization of a phase relaxation model with temperature dependent convection and reaction. The model consists of a diffusion-advection PDE for temperature and an ODE with double obstacle for phase variable. Under a stability constraint, this scheme is shown to converge with optimal orders for temperature and enthalpy, and for heat flux as time-step .
In this paper we certify that the same approach proposed in previous works by Chniti et al. [C. R. Acad. Sci. 342 (2006) 883–886; CALCOLO 45 (2008) 111–147; J. Sci. Comput. 38 (2009) 207–228] can be applied to more general operators with strong heterogeneity in the coefficients. We consider here the case of reaction-diffusion problems with piecewise constant coefficients. The problem reduces to determining the coefficients of some transmission conditions to obtain fast convergence of domain decomposition...
In this paper we certify that the same approach proposed in previous works by Chniti et al. [C. R. Acad. Sci.342 (2006) 883–886; CALCOLO45 (2008) 111–147; J. Sci. Comput.38 (2009) 207–228] can be applied to more general operators with strong heterogeneity in the coefficients. We consider here the case of reaction-diffusion problems with piecewise constant coefficients. The problem reduces to determining the coefficients of some transmission conditions to obtain fast convergence of domain decomposition...
We prove a maximum principle for linear second order elliptic systems in divergence form with discontinuous coefficients under a suitable condition on the dispersion of the eigenvalues of the coefficients matrix.