An index for global Hopf bifurcation in parabolic systems.
An initial-boundary value problem for quasi-linear parabolic systems of higher order
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 overlapping additive Schwarz-Richardson method for monotone nonlinear parabolic problems.
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 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...
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 L2 x L∞ 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 H1 x H1 ∩ L∞. A family of fully...
Analysis of the DGFEM for nonlinear convection-diffusion problems.
Analysis of the free boundary for the p-parabolic variational problem (p ≥ 2).
Abstract Variational inequalities (free boundaries), governed by the p-parabolic equation (p > 2), are the objects of investigation in this paper. Using intrinsic scaling we establish the behavior of solutions near the free boundary. A consequence of this is that the time levels of the free boundary are porous (in N-dimension) and therefore its Hausdorff dimension is less than N. In particular the N-Lebesgue measure of the free boundary is zero for each t-level.
Analysis tools for finite volume schemes
Analytic solutions for the classical two-phase Stefan problem
Analytical results on a model for damaging in domains and interfaces
This paper deals with a model describing damage processes in a (nonlinear) elastic body which is in contact with adhesion with a rigid support. On the basis of phase transitions theory, we detail the derivation of the model written in terms of a PDE system, combined with suitable initial and boundary conditions. Some internal constraints on the variables are introduced in the equations and on the boundary, to get physical consistency. We prove the existence of global in time solutions (to a suitable...
Analytical results on a model for damaging in domains and interfaces*
This paper deals with a model describing damage processes in a (nonlinear) elastic body which is in contact with adhesion with a rigid support. On the basis of phase transitions theory, we detail the derivation of the model written in terms of a PDE system, combined with suitable initial and boundary conditions. Some internal constraints on the variables are introduced in the equations and on the boundary, to get physical consistency. We prove the existence of global in time solutions (to a suitable...
Ancora sulla perturbazione delle disequazioni d'evoluzione paraboliche
Anisotropic parabolic problems with slowly or rapidly growing terms
We consider an abstract parabolic problem in a framework of maximal monotone graphs, possibly multi-valued, with growth conditions formulated with the help of an x-dependent N-function. The main novelty of the paper consists in the lack of any growth restrictions on the N-function combined with its anisotropic character, namely we allow the dependence on all the directions of the gradient, not only on its absolute value. This leads to using the notion of modular convergence and studying in detail...