Remarks on the asymptotical behaviour of solutions to some nonlinear parabolic equations
Remarks on the large time behaviour of a nonlinear diffusion equation
Remarks on the smoothness of the solutions of the 3-D Navier-Stokes equations.
Remarks on weak solutions for a nonlocal parabolic problem.
Renormalized entropy solutions for degenerate nonlinear evolution problems.
Results on existence of solution for an optimal design problem.
In this paper we study a control problem for elliptic nonlinear monotone problems with Dirichlet boundary conditions where the control variables are the coefficients of the equation and the open set where the partial differential problem is studied.
Rigorous numerics for the Cahn-Hilliard equation on the unit square.
Robust estimates of certain large deviation probabilities for controlled semi-martingales
Motivated by downside risk minimization on the wealth process in an incomplete market model, we have studied in the recent work the asymptotic behavior as time horizon T → ∞ of the minimizing probability that the empirical mean of a controlled semi-martingale falls below a certain level on the time horizon T. This asymptotic behavior relates to a risk-sensitive stochastic control problem in the risk-averse case. Indeed, we obtained an expression of the decay rate of the probability by the Legendre...
Root growth: homogenization in domains with time dependent partial perforations
In this article we derive a macroscopic model for the time evolution of root density, starting from a discrete mesh of roots, using homogenization techniques. In the microscopic model each root grows vertically according to an ordinary differential equation. The roots growth rates depend on the spatial distribution of nutrient in the soil, which also evolves in time, leading to a fully coupled non-linear problem. We derive an effective partial differential equation for the root tip surface and for...
Root growth: homogenization in domains with time dependent partial perforations
In this article we derive a macroscopic model for the time evolution of root density, starting from a discrete mesh of roots, using homogenization techniques. In the microscopic model each root grows vertically according to an ordinary differential equation. The roots growth rates depend on the spatial distribution of nutrient in the soil, which also evolves in time, leading to a fully coupled non-linear problem. We derive an effective partial differential equation for the root tip surface and for...
Root growth: homogenization in domains with time dependent partial perforations
In this article we derive a macroscopic model for the time evolution of root density, starting from a discrete mesh of roots, using homogenization techniques. In the microscopic model each root grows vertically according to an ordinary differential equation. The roots growth rates depend on the spatial distribution of nutrient in the soil, which also evolves in time, leading to a fully coupled non-linear problem. We derive an effective partial differential equation for the root tip surface and for...
Rothe time-discretization method for the semilinear heat equation subject to a nonlocal boundary condition.
Scaling in nonlinear parabolic equations: locality versus globality
Scaling limits and regularity results for a class of Ginzburg-Landau systems
Scattering theory for Hartree type equations
Scattering, transformations spectrales et équations d'évolution non linéaire II
Second order parabolic systems, optimal regularity, and singular sets of solutions
Segmentation of MRI data by means of nonlinear diffusion
The article focuses on the application of the segmentation algorithm based on the numerical solution of the Allen-Cahn non-linear diffusion partial differential equation. This equation is related to the motion of curves by mean curvature. It exhibits several suitable mathematical properties including stable solution profile. This allows the user to follow accurately the position of the segmentation curve by bringing it quickly to the vicinity of the segmented object and by approaching the details...
Self-similar singular solution of doubly singular parabolic equation with gradient absorption term.
Self-similar solutions for a nonlinear degenerate parabolic equation.