Failure of convergence of the Lax-Oleinik semi-group in the time periodic case
First-order systems of linear partial differential equations: normal forms, canonical systems, transform methods
In this paper we consider first-order systems with constant coefficients for two real-valued functions of two real variables. This is both a problem in itself, as well as an alternative view of the classical linear partial differential equations of second order with constant coefficients. The classification of the systems is done using elementary methods of linear algebra. Each type presents its special canonical form in the associated characteristic coordinate system. Then you can formulate initial...
Flabbiness for solution sheaves of microdifferential systems
Formation of singularities for viscosity solutions of Hamilton-Jacobi equations
Formes bilinéaires compatibles avec un système
Free Boundary Problems Associated with Multiscale Tumor Models
The present paper introduces a tumor model with two time scales, the time t during which the tumor grows and the cycle time of individual cells. The model also includes the effects of gene mutations on the population density of the tumor cells. The model is formulated as a free boundary problem for a coupled system of elliptic, parabolic and hyperbolic equations within the tumor region, with nonlinear and nonlocal terms. Existence and uniqueness theorems are proved, and properties of the free boundary...
Frentes de explosión en ecuaciones de Hamilton Jacobi por argumentos de control determinista.
Functional differential equations with non-local boundary conditions.
Funzioni -convesse
We study a class of functions which differ essentially from those which are the sum of a convex function and a regular one and which have interesting properties related to -convergence and to problems with non-convex constraints. In particular some results are given for the associated evolution equations.