Local solvability of degenerate Monge-Ampère equations and applications to geometry.
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.
On a Kirchhoff-Carrier equation with nonlinear terms containing a finite number of unknown values
We consider problem (P) of Kirchhoff-Carrier type with nonlinear terms containing a finite number of unknown values with By applying the linearization method together with the Faedo-Galerkin method and the weak compact method, we first prove the existence and uniqueness of a local weak solution of problem (P). Next, we consider a specific case of (P) in which the nonlinear term contains the sum . Under suitable conditions, we prove that the solution of converges to the solution of the corresponding...
On a mixed problem for a coupled nonlinear system.
On a nonlocal problem for a confined plasma in a Tokamak
The paper deals with a nonlocal problem related to the equilibrium of a confined plasma in a Tokamak machine. This problem involves terms and , which are neither local, nor continuous, nor monotone. By using the Galerkin approximate method and establishing some properties of the decreasing rearrangement, we prove the existence of solutions to such problem.