Ricerc@Sapienza

The basic investigation is the existence and the (numerical) observability of propagating fronts in the framework of the so-called Epithelial-to-Mesenchymal Transition and its reverse Mesenchymal-to-Epithelial Transition, which are known to play a crucial role in tumor development. To this aim, we propose a simplified one-dimensional hyperbolic-parabolic PDE model composed of two equations, one for the representative of the epithelial phenotype, and the second describing the mesenchymal phenotype.

In this paper we consider a class of “filtered” schemes for some first order time dependent Hamilton-Jacobi equations. A typical feature of a filtered scheme is that at the node xj the scheme is obtained as a mixture of a high-order scheme and a

We present a nite difference method to compute the principal eigenvalue and the
corresponding eigenfunction for a large class of second order elliptic operators including notably linear
operators in non divergence form and fully nonlinear operators.
The principal eigenvalue is computed by solving a nite-dimensional nonlinear min-max optimization
problem. We prove the convergence of the method and we discuss its implementation. Some examples
where the exact solution is explicitly known show the effectiveness of the method.