Mathematical analysis of a finite element method without spurious solutions for computation of dielectric waveguides.
Mathematical and numerical approaches for multiscale problems
Mathematical modeling of antigenicity for HIV dynamics
This contribution is devoted to a new model of HIV multiplication motivated by the patent of one of the authors. We take into account the antigenic diversity through what we define “antigenicity”, whether of the virus or of the adapted lymphocytes. We model the interaction of the immune system and the viral strains by two processes. On the one hand, the presence of a given viral quasi-species generates antigenically adapted lymphocytes. On the other hand, the lymphocytes kill only viruses for which...
Modelling of multicomponent diffusive phase transformation in solids
Physical analysis of phase transformation of materials consisting from several (both substitutional and interstitial) components, coming from the Onsager extremal thermodynamic principle, leads, from the mathematical point of view, to a system of partial differential equations of evolution type, including certain integral term, with substantial differences in particular phases (, ) and in moving interface of finite thickness (), in whose center the ideal liquid material behaviour can be detected....