Le problème mixte des équations des ondes et applications
Linear scheme for finite element solution of nonlinear parabolic-elliptic problems with nonhomogeneous Dirichlet boundary condition
The computation of nonlinear quasistationary two-dimensional magnetic fields leads to a nonlinear second order parabolic-elliptic initial-boundary value problem. Such a problem with a nonhomogeneous Dirichlet boundary condition on a part of the boundary is studied in this paper. The problem is discretized in space by the finite element method with linear functions on triangular elements and in time by the implicit-explicit method (the left-hand side by the implicit Euler method and the right-hand...
Local solvability of degenerate Monge-Ampère equations and applications to geometry.
Local well-posedness of solutions to 2D magnetic Prandtl model in the Prandtl-Hartmann regime
We consider the 2D magnetic Prandtl equation in the Prandtl-Hartmann regime in a periodic domain and prove the local existence and uniqueness of solutions by energy methods in a polynomial weighted Sobolev space. On the one hand, we have noted that the -derivative of the pressure plays a key role in all known results on the existence and uniqueness of solutions to the Prandtl-Hartmann regime equations, in which the case of favorable
Mathematical and numerical analysis of a stratigraphic model
In this paper, we consider a multi-lithology diffusion model used in stratigraphic modelling to simulate large scale transport processes of sediments described as a mixture of lithologies. This model is a simplified one for which the surficial fluxes are proportional to the slope of the topography and to a lithology fraction with unitary diffusion coefficients. The main unknowns of the system are the sediment thickness , the surface concentrations in lithology of the sediments at the top...
Mathematical and numerical analysis of a stratigraphic model
In this paper, we consider a multi-lithology diffusion model used in stratigraphic modelling to simulate large scale transport processes of sediments described as a mixture of L lithologies. This model is a simplified one for which the surficial fluxes are proportional to the slope of the topography and to a lithology fraction with unitary diffusion coefficients. The main unknowns of the system are the sediment thickness h, the L surface concentrations in lithology i of the sediments at the...
Mathematical framework for current density imaging due to discharge of electro-muscular disruption devices
Electro-muscular disruption (EMD) devices such as TASER M26 and X26 have been used as a less-than-lethal weapon. Such EMD devices shoot a pair of darts toward an intended target to generate an incapacitating electrical shock. In the use of the EMD device, there have been controversial questions about its safety and effectiveness. To address these questions, we need to investigate the distribution of the current density J inside the target produced by the EMD device. One approach is to develop a computational...
Mathematical modelling and numerical solution of swelling of cartilaginous tissues. Part II: Mixed-hybrid finite element solution
The swelling and shrinkage of biological tissues are modelled by a four-component mixture theory [J.M. Huyghe and J.D. Janssen, Int. J. Engng. Sci.35 (1997) 793–802; K. Malakpoor, E.F. Kaasschieter and J.M. Huyghe, Mathematical modelling and numerical solution of swelling of cartilaginous tissues. Part I: Modeling of incompressible charged porous media. ESAIM: M2AN41 (2007) 661–678]. This theory results in a coupled system of nonlinear parabolic differential equations together with an algebraic...
Mixed problem for semilinear hyperbolic equation of second order with the Dirichlet boundary condition (Preliminary communication)
Mixed problem with integral boundary condition for a high order mixed type partial differential equation.
Mixed problem with nonlocal boundary conditions for a third-order partial differential equation of mixed type.
Morawetz problem for generalized Tricomi equation.
Nonlinear symmetric positive systems
Nonlocal boundary value problems for elliptic-parabolic differential and difference equations.
Non-local problems for parabolic-hyperbolic equations with deviation from the characteristics and three type-changing lines.
Nonsteady flow of water and oil through inhomogeneous porous media
Nouveaux problèmes sur les équations mixtes
Numerical analysis of nonlinear elliptic-parabolic equations
This paper deals with the numerical approximation of mild solutions of elliptic-parabolic equations, relying on the existence results of Bénilan and Wittbold (1996). We introduce a new and simple algorithm based on Halpern’s iteration for nonexpansive operators (Bauschke, 1996; Halpern, 1967; Lions, 1977), which is shown to be convergent in the degenerate case, and compare it with existing schemes (Jäger and Kačur, 1995; Kačur, 1999).
Numerical analysis of nonlinear elliptic-parabolic equations
This paper deals with the numerical approximation of mild solutions of elliptic-parabolic equations, relying on the existence results of Bénilan and Wittbold (1996). We introduce a new and simple algorithm based on Halpern's iteration for nonexpansive operators (Bauschke, 1996; Halpern, 1967; Lions, 1977), which is shown to be convergent in the degenerate case, and compare it with existing schemes (Jäger and Kačur, 1995; Kačur, 1999).
Oblique derivative problems for generalized Rassias equations of mixed type with several characteristic boundaries.