An Isoperimetric Inequality for the Principal Eigenvalue of a Periodic-Parabolic Problem.
An iteration method for controllability of semilinear parabolic equations.
An -approach for the study of degenerate parabolic equations.
An observability estimate for parabolic equations from a measurable set in time and its applications
This paper presents a new observability estimate for parabolic equations in , where is a convex domain. The observation region is restricted over a product set of an open nonempty subset of and a subset of positive measure in . This estimate is derived with the aid of a quantitative unique continuation at one point in time. Applications to the bang-bang property for norm and time optimal control problems are provided.
An operator-splitting Galerkin/SUPG finite element method for population balance equations : stability and convergence
We present a heterogeneous finite element method for the solution of a high-dimensional population balance equation, which depends both the physical and the internal property coordinates. The proposed scheme tackles the two main difficulties in the finite element solution of population balance equation: (i) spatial discretization with the standard finite elements, when the dimension of the equation is more than three, (ii) spurious oscillations in the solution induced by standard Galerkin approximation...
An operator-splitting Galerkin/SUPG finite element method for population balance equations : stability and convergence
We present a heterogeneous finite element method for the solution of a high-dimensional population balance equation, which depends both the physical and the internal property coordinates. The proposed scheme tackles the two main difficulties in the finite element solution of population balance equation: (i) spatial discretization with the standard finite elements, when the dimension of the equation is more than three, (ii) spurious oscillations in...
An Optimal Control Problem for a Predator-Prey Reaction-Diffusion System
An optimal control problem is studied for a predator-prey system of PDE, with a logistic growth rate of the prey and a general functional response of the predator. The control function has two components. The purpose is to maximize a mean density of the two species in their habitat. The existence of the optimal solution is analyzed and some necessary optimality conditions are established. The form of the optimal control is found in some particular...
An optimal error bound for a finite element approximation of a model for phase separation of a multi-component alloy with non-smooth free energy
Using the approach in [5] for analysing time discretization error and assuming more regularity on the initial data, we improve on the error bound derived in [2] for a fully practical piecewise linear finite element approximation with a backward Euler time discretization of a model for phase separation of a multi-component alloy with non-smooth free energy.
An Optimal Regularity Result For A Class Of Quasilinear Parabolic Systems.
An optimal strong equilibrium solution for cooperative multi-leader-follower Stackelberg Markov chains games
This paper presents a novel approach for computing the strong Stackelberg/Nash equilibrium for Markov chains games. For solving the cooperative -leaders and -followers Markov game we consider the minimization of the norm that reduces the distance to the utopian point in the Euclidian space. Then, we reduce the optimization problem to find a Pareto optimal solution. We employ a bi-level programming method implemented by the extraproximal optimization approach for computing the strong Stackelberg/Nash...
An overlapping additive Schwarz-Richardson method for monotone nonlinear parabolic problems.
An unconditionally stable finite element scheme for anisotropic curve shortening flow
Based on a recent novel formulation of parametric anisotropic curve shortening flow, we analyse a fully discrete numerical method of this geometric evolution equation. The method uses piecewise linear finite elements in space and a backward Euler approximation in time. We establish existence and uniqueness of a discrete solution, as well as an unconditional stability property. Some numerical computations confirm the theoretical results and demonstrate the practicality of our method.
Analyse de sensibilité d’un problème de contrôle optimal bilinéaire
Dans cet article, nous étudions la sensibilité d’un problème de contrôle optimal de type bilinéaire. Le coût est différentiable, quadratique et strictement convexe. Le système est gouverné par un opérateur parabolique du quatrième ordre et présente une perturbation additive dans l’équation d’état, ainsi qu’une partie bilinéaire, relativement au contrôle et à l’état , de la forme . Sous des conditions de petitesse de l’état initial et de la perturbation, nous exploitons les propriétés de régularité...
Analyse mathématique des transferts thermiques dans des systèmes dispersés subissant des transformations de phases
Analysis and numerical solution of a nonlinear cross-diffusion system arising in population dynamics.
En este trabajo se estudia de modo analítico y numérico un problema en ecuaciones diferenciales en derivadas parciales que modela la dinámica de dos poblaciones afectadas por la presión poblacional inter e intraespecíficas y por un potencial medioambiental. Debido a los términos de difusión cruzada, el problema es fuertemente no lineal por lo que el principio del máximo y los métodos relacionados con el mismo no pueden ser aplicados. En primer lugar demostramos la existencia de soluciones débiles...
Analysis of a combined barycentric finite volume—nonconforming finite element method for nonlinear convection-diffusion problems
We present the convergence analysis of an efficient numerical method for the solution of an initial-boundary value problem for a scalar nonlinear conservation law equation with a diffusion term. Nonlinear convective terms are approximated with the aid of a monotone finite volume scheme considered over the finite volume barycentric mesh, whereas the diffusion term is discretized by piecewise linear nonconforming triangular finite elements. Under the assumption that the triangulations are of weakly...
Analysis of a Non-Linear Difference scheme in Reaction-Diffusion.
Analysis of a semidiscrete scheme for solving image smoothing equation of mean curvature flow type.
Analysis of a time discretization scheme for a nonstandard viscous Cahn–Hilliard system
In this paper we propose a time discretization of a system of two parabolic equations describing diffusion-driven atom rearrangement in crystalline matter. The equations express the balances of microforces and microenergy; the two phase fields are the order parameter and the chemical potential. The initial and boundary-value problem for the evolutionary system is known to be well posed. Convergence of the discrete scheme to the solution of the continuous problem is proved by a careful development...
Analysis of gradient flow of a regularized Mumford-Shah functional for image segmentation and image inpainting
This paper studies the gradient flow of a regularized Mumford-Shah functional proposed by Ambrosio and Tortorelli (1990, 1992) for image segmentation, and adopted by Esedoglu and Shen (2002) for image inpainting. It is shown that the gradient flow with initial data possesses a global weak solution, and it has a unique global in time strong solution, which has at most finite number of point singularities in the space-time, when the initial data are in . A family of fully discrete approximation...