A boundary blow-up for sub-linear elliptic problems with a nonlinear gradient term.
A FETI-DP preconditioner for mortar methods in three dimensions.
A free boundary problem for a nonlinear degenerate elliptic system modeling a thermistor
A global branch of steady vortex rings.
A Hamilton-Jacobi approach to junction problems and application to traffic flows
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...
A matching of singularities in domain decomposition methods for reaction-diffusion problems with discontinuous coefficients
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...
A matching of singularities in domain decomposition methods for reaction-diffusion problems with discontinuous coefficients
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...
A maximum principle for linear elliptic systems with discontinuous coefficients
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.
A multilevel adaptive mesh generation scheme using Kd-trees.
A note about a priori estimates for indefinite problems in unbounded domains.
A parabolic differential equation with unbounded piecewise constant delay.
A parabolic-hyperbolic free boundary problem modeling tumor growth with drug application.
A parametrix construction for wave equations with coefficients
In this article we give a construction of the wave group for variable coefficient, time dependent wave equations, under the hypothesis that the coefficients of the principal term possess two bounded derivatives in the spatial variables, and one bounded derivative in the time variable. We use this construction to establish the Strichartz and Pecher estimates for solutions to the Cauchy problem for such equations, in space dimensions and .
A Riemann problem with small viscosity and dispersion.
A Transmission Strategy for Hyperbolic Internal Waves of Small Width
Semilinear hyperbolic problems with source terms piecewise smooth and discontinuous across characteristic surfaces yield similarly piecewise smooth solutions. If the discontinuous source is replaced with a smooth transition layer, the discontinuity of the solution is replaced by a smooth internal layer. In this paper we describe how the layer structure of the solution can be computed from the layer structure of the source in the limit of thin layers. The key idea is to use a transmission problem...
A variational approach for a semi-linear parabolic equation with measure data
Algèbres différentielles et problème de Goursat non linéaire à données irrégulières
An additive Schwarz method for mortar Morley finite element discretizations of 4th order elliptic problem in 2D.
An -theory of existence and uniqueness of solutions of nonlinear elliptic equations
An overlapping additive Schwarz-Richardson method for monotone nonlinear parabolic problems.