Nontrivial solution for a nonlocal elliptic transmission problem in variable exponent Sobolev spaces.
Non-unicité du problème de Cauchy pour des opérateurs de type principal
Non-Uniqueness and Uniqueness in the Cauchy Problem at Simple Characteristic Points.
Non-uniqueness in a free boundary problem.
Nonuniqueness in the martingale problem and the Dirichlet problem for uniformly elliptic operators
Normale Auflösbarkeit bei linearen partiellen Differentialoperatoren in lokalen gewichteten Sobolevräumen.
Note on nonlinear semigroups and free boundary problem for controlled Markov processes
Novel criteria on global robust exponential stability to a class of reaction-diffusion neural networks with delays.
Numerical approximations of parabolic differential functional equations with the initial boundary conditions of the Neumann type
The aim of this paper is to present a numerical approximation for quasilinear parabolic differential functional equations with initial boundary conditions of the Neumann type. The convergence result is proved for a difference scheme with the property that the difference operators approximating mixed derivatives depend on the local properties of the coefficients of the differential equation. A numerical example is given.
Numerical Approximations of the Relative Rearrangement: The piecewise linear case. Application to some Nonlocal Problems
We first prove an abstract result for a class of nonlocal problems using fixed point method. We apply this result to equations revelant from plasma physic problems. These equations contain terms like monotone or relative rearrangement of functions. So, we start the approximation study by using finite element to discretize this nonstandard quantities. We end the paper by giving a numerical resolution of a model containing those terms.
Numerical computations for solidification problems with change of volume
Numerical identification of a coefficient in a parabolic quasilinear equation
In the article the following optimal control problem is studied: to determine a certain coefficient in a quasilinear partial differential equation of parabolic type so that the solution of a boundary value problem for this equation would minimise a given integral functional. In addition to the design and analysis of a numerical method the paper contains the solution of the fundamental problems connected with the formulation of the problem in question (existence and uniqueness of the solution of...
Numerical method of identification of an unknown source term in a heat equation.
Numerical methods for phase transition problems
Nel presente articolo si illustrano alcuni dei principali metodi numerici per l'approssimazione di modelli matematici legati ai fenomeni di transizione di fase. Per semplificare e contenere l'esposizione ci siamo limitati a discutere con un certo dettaglio i metodi più recenti, presentandoli nel caso di problemi modello, quali il classico problema di Stefan e l'evoluzione di superficie per curvatura media, solo accennando alle applicazioni e modelli più generali.
Numerical realization of the Bayesian inversion accelerated using surrogate models
The Bayesian inversion is a natural approach to the solution of inverse problems based on uncertain observed data. The result of such an inverse problem is the posterior distribution of unknown parameters. This paper deals with the numerical realization of the Bayesian inversion focusing on problems governed by computationally expensive forward models such as numerical solutions of partial differential equations. Samples from the posterior distribution are generated using the Markov chain Monte...
Numerical Solution of a Hyperbolic Free Boundary Problem with a Method of Characteristics.
Numerical solution of an inverse initial boundary value problem for the wave equation in the presence of conductivity imperfections of small volume
We consider the numerical solution, in two- and three-dimensional bounded domains, of the inverse problem for identifying the location of small-volume, conductivity imperfections in a medium with homogeneous background. A dynamic approach, based on the wave equation, permits us to treat the important case of “limited-view” data. Our numerical algorithm is based on the coupling of a finite element solution of the wave equation, an exact controllability method and finally a Fourier inversion for localizing...
Numerical solution of an inverse initial boundary value problem for the wave equation in the presence of conductivity imperfections of small volume
We consider the numerical solution, in two- and three-dimensional bounded domains, of the inverse problem for identifying the location of small-volume, conductivity imperfections in a medium with homogeneous background. A dynamic approach, based on the wave equation, permits us to treat the important case of “limited-view” data. Our numerical algorithm is based on the coupling of a finite element solution of the wave equation, an exact controllability method and finally a Fourier inversion for...
Numerical Solution of Steady-State Porous Flow Free Boundary Problems.
Numerical solutions of a fractional predator-prey system.