We analyse the large-time asymptotics of quasilinear (possibly) degenerate parabolic systems in three cases: 1) scalar problems with con®nement by a uniformly convex potential, 2) uncon®ned scalar… (More)

A new approach to the construction of entropies and entropy productions for a large class of nonlinear evolutionary PDEs of even order in one space dimension is presented. The task of proving entropy… (More)

The global-in-time existence of weak solutions to the barotropic compressible quantum Navier-Stokes equations in a three-dimensional torus for large data is proved. The model consists of the mass… (More)

Abstract. The global existence of a non-negative weak solution to a multi-dimensional parabolic strongly coupled model for two competing species is proved. The main feature of the model is that the… (More)

The global existence of non-negative weak solutions to a strongly coupled parabolic system arising in population dynamics is shown. The cross-diffusion terms are allowed to be arbitrarily large,… (More)

A nonlinear Black-Scholes equation which models transaction costs arising in the hedging of portfolios is discretized semi-implicitly using high order compact finite difference schemes. In… (More)

The quantum Euler-Poisson model for semiconductors is considered on spatial bounded domain. The equations take the form of Euler-Poisson forced by quantum Bohm potential. In [20], the well-posedness… (More)

Energy-transport models are used in semiconductor simulations to account for thermal effects. The model consists of the continuity equations for the number and energy of the electrons, coupled to the… (More)