Corrado Mascia

Pauline Lafitte, Corrado Mascia

We analyze numerically a forward-backward diffusion equation with a cubic-like diffusion function, -emerging in the framework of phase transitions modeling- and its "entropy" formulation determined by considering it as the singular limit of a third-order pseudo-parabolic equation. Precisely, we propose schemes for both the second and the third order equations, we discuss the analytical properties of their semi-discrete counter-parts and we compare the numerical results in the case of initial data of Riemann type, showing strengths and flaws of the two approaches, the main emphasis being given to the propagation of transition interfaces.

Corrado Lattanzio, Corrado Mascia, Ramón G. Plaza et al.

This paper deals with the numerical (finite volume) approximation of reaction-diffusion systems with relaxation, among which the hyperbolic extension of the Allen--Cahn equation represents a notable prototype. Appropriate discretizations are constructed starting from the kinetic interpretation of the model as a particular case of reactive jump process. Numerical experiments are provided for exemplifying the theoretical analysis (previously developed by the same authors) concerning the stability of traveling waves, and important evidence of the validity of those results beyond the formal hypotheses is numerically established.

Pierfrancesco Moschetta, Corrado Mascia

A Predictor-Corrector strategy is employed for the numerical simulation of the one-dimensional Burridge-Knopoff model of earthquakes. This approach is totally explicit and allows to reproduce the main features of the model. The results achieved are compared with those of several previous works available in the literature, in order to state the effectiveness of the novel numerical strategy. Simulations are performed starting from the simplest cases and are aimed at studying the qualitative trends of the phenomena under analysis. By increasing the size of the associated differential system, it is possible to examine data on the basis of the Gutenberg-Richter statistical law. Finally, some tests are conducted to investigate the continuum limit of the discrete Burridge-Knopoff model towards a macroscopic dynamics.