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.
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.
Semi-analytical approach to initial problems for systems of nonlinear partial differential equations with constant delay
This paper deals with the differential transform method for solving of an initial value problem for a system of two nonlinear functional partial differential equations of parabolic type. We consider non-delayed as well as delayed types of coupling and the different variety of initial functions are thought over. The convergence of solutions and the error estimation to the presented procedure is studied. Two numerical examples for non-delayed and delayed systems are included.
Semi-classical analysis and vanishing properties of solutions to quasilinear equations.
Semilinear parabolic problems on manifolds and applications to the non-compact Yamabe problem.
Semilineare parabolische Differentialgleichungen mit starker Nichtlinearität.
Sets of admissible initial data for porous-medium equations with absorption.
Similarity stabilizes blow-up
The blow-up of solutions to a quasilinear heat equation is studied using a similarity transformation that turns the equation into a nonlocal equation whose steady solutions are stable. This allows energy methods to be used, instead of the comparison principles used previously. Among the questions discussed are the time and location of blow-up of perturbations of the steady blow-up profile.
Single input controllability of a simplified fluid-structure interaction model
In this paper we study a controllability problem for a simplified one dimensional model for the motion of a rigid body in a viscous fluid. The control variable is the velocity of the fluid at one end. One of the novelties brought in with respect to the existing literature consists in the fact that we use a single scalar control. Moreover, we introduce a new methodology, which can be used for other nonlinear parabolic systems, independently of the techniques previously used for the linearized problem....
Single-point blow-up for a semilinear parabolic system
We consider positive solutions of the system ; in a ball or in the whole space, with . Relatively little is known on the blow-up set for semilinear parabolic systems and, up to now, no result was available for this basic system except for the very special case . Here we prove single-point blow-up for a large class of radial decreasing solutions. This in particular solves a problem left open in a paper of A. Friedman and Y. Giga (1987). We also obtain lower pointwise estimates for the final...
Singular integral inequalities and stability of semilinear parabolic equations
Using a method developed by the author for an analysis of singular integral inequalities a stability theorem for semilinear parabolic PDEs is proved.