Darcy's law in anisothermic porous medium.
Decay estimates of heat transfer to melton polymer flow in pipes with viscous dissipation.
Definitions of standard stress and standard heat flux, in simple bodies, treated according to Mach and Painlevé
Derivation of a homogenized two-temperature model from the heat equation
This work studies the heat equation in a two-phase material with spherical inclusions. Under some appropriate scaling on the size, volume fraction and heat capacity of the inclusions, we derive a coupled system of partial differential equations governing the evolution of the temperature of each phase at a macroscopic level of description. The coupling terms describing the exchange of heat between the phases are obtained by using homogenization techniques originating from [D. Cioranescu, F. Murat,...
Diffuse-interface treatment of the anisotropic mean-curvature flow
We investigate the motion by mean curvature in relative geometry by means of the modified Allen-Cahn equation, where the anisotropy is incorporated. We obtain the existence result for the solution as well as a result concerning the asymptotical behaviour with respect to the thickness parameter. By means of a numerical scheme, we can approximate the original law, as shown in several computational examples.
Diffusion with dissolution and precipitation in a porous medium: Mathematical analysis and numerical approximation of a simplified model
Modeling the kinetics of a precipitation dissolution reaction occurring in a porous medium where diffusion also takes place leads to a system of two parabolic equations and one ordinary differential equation coupled with a stiff reaction term. This system is discretized by a finite volume scheme which is suitable for the approximation of the discontinuous reaction term of unknown sign. Discrete solutions are shown to exist and converge towards a weak solution of the continuous problem. Uniqueness...
Direct approach to mean-curvature flow with topological changes
This contribution deals with the numerical simulation of dislocation dynamics. Dislocations are described by means of the evolution of a family of closed or open smooth curves , . The curves are driven by the normal velocity which is the function of curvature and the position. The evolution law reads as: . The motion law is treated using direct approach numerically solved by two schemes, i. e., backward Euler semi-implicit and semi-discrete method of lines. Numerical stability is improved...
Dos algoritmos para la resolución numérica de una ecuación parabólica casi-lineal.
Dynamic optimal cooling control for continuous casting of steel
Dynamic pressure in relativistic thermodynamics
Dynamics of a system of nonlinear differential equations.