Regular regions for parabolic and elliptic equations
Regularity estimates in Besov spaces for initial-value problems of general parabolic equations.
Regularity for entropy solutions of a class of parabolic equations with irregular data
Using as a main tool the time-regularizing convolution operator introduced by R. Landes, we obtain regularity results for entropy solutions of a class of parabolic equations with irregular data. The results are obtained in a very general setting and include known previous results.
Regularity in free boundary problems
Regularity of the free boundary for non degenerate phase transition problems of parabolic type
Regularization method for parabolic equation with variable operator.
Remarks on a nonlocal problem involving the Dirichlet energy
Remarks on non controllability of the heat equation with memory
In this paper we deal with the null controllability problem for the heat equation with a memory term by means of boundary controls. For each positive final time T and when the control is acting on the whole boundary, we prove that there exists a set of initial conditions such that the null controllability property fails.
Remarks on Parameter Identification. I.
Remarks on weak solutions for a nonlocal parabolic problem.
Resolvent positive operators and inhomogeneous boundary conditions
Reverse smoothing effects, fine asymptotics, and Harnack inequalities for fast diffusion equations.
Rothe method for a mixed problem with an integral condition for the two-dimensional diffusion equation.
Rothe time-discretization method for a nonlocal problem arising in thermoelasticity.
Rothe's method for degenerate quasilinear parabolic equations
Schéma des différences finies pour un système d'équations paraboliques non linéaires avec dérivées mixtes
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...
Semiclassical limit of a simplified quantum energy-transport model for bipolar semiconductors
We are concerned with a simplified quantum energy-transport model for bipolar semiconductors, which consists of nonlinear parabolic fourth-order equations for the electron and hole density; degenerate elliptic heat equations for the electron and hole temperature; and Poisson equation for the electric potential. For the periodic boundary value problem in the torus , the global existence of weak solutions is proved, based on a time-discretization, an entropy-type estimate, and a fixed-point argument....
Semidiscretization for a nonlocal parabolic problem.
Short-time heat flow and functions of bounded variation in
We prove a characterisation of sets with finite perimeter and functions in terms of the short time behaviour of the heat semigroup in . For sets with smooth boundary a more precise result is shown.