Saddle-point problems in partial differential equations and applications to linear quadratic differential games
Scaling in nonlinear parabolic equations: locality versus globality
Scaling limits and regularity results for a class of Ginzburg-Landau systems
Scalings in homogenisation of reaction, diffusion and interfacial exchange in a two-phase medium
Scattering theory for Hartree type equations
Scattering, transformations spectrales et équations d'évolution non linéaire II
Schauder estimates for a class of degenerate elliptic and parabolic operators with unbounded coefficients in
Schauder theorems for linear elliptic and parabolic problems with unbounded coefficients in
We study existence, uniqueness, and smoothing properties of the solutions to a class of linear second order elliptic and parabolic differential equations with unbounded coefficients in . The main results are global Schauder estimates, which hold in spite of the unboundedness of the coefficients.
Schéma des différences finies pour un système d'équations paraboliques non linéaires avec dérivées mixtes
Schema explicite des différences finies pour un système d'équations non linéaires du type parabolique avec des conditions aux limites non linéaires
Second order parabolic equations and weak uniqueness of diffusions with discontinuous coefficients
We prove the unique solvability of parabolic equations with discontinuous leading coefficients in . Using this result, we establish the uniqueness of diffusion processes with time-dependent discontinuous coefficients.
Second order parabolic systems, optimal regularity, and singular sets of solutions
Second order unbounded parabolic equations in separated form
We prove existence and uniqueness of viscosity solutions of Cauchy problems for fully nonlinear unbounded second order Hamilton-Jacobi-Bellman-Isaacs equations defined on the product of two infinite-dimensional Hilbert spaces H'× H'', where H'' is separable. The equations have a special "separated" form in the sense that the terms involving second derivatives are everywhere defined, continuous and depend only on derivatives with respect to x'' ∈ H'', while the unbounded terms are of first order...
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.
Self-similar solutions for the two-dimensional Nernst-Planck-Debye system
We investigate the two-component Nernst-Planck-Debye system by a numerical study of self-similar solutions using the Runge-Kutta method of order four and comparing the results obtained with the solutions of a one-component system. Properties of the solutions indicated by numerical simulations are proved and an existence result is established based on comparison arguments for singular ordinary differential equations.
Self-similar solutions in reaction-diffusion systems
In this paper we examine self-similar solutions to the system , i = 1,…,m, , t > 0, , i = 1,…,m, , where m > 1 and , to describe asymptotics near the blow up point.
Self-similar solutions of convection-diffusion processes.
Self-similarity in chemotaxis systems
We consider a system which describes the scaling limit of several chemotaxis systems. We focus on self-similarity, and review some recent results on forward and backward self-similar solutions to the system.