The book is devoted to the theory of gradient flows in the general framework of metric
spaces, and in the more specific setting of the space of probability measures, which provide …

We analyse the large-time asymptotics of quasilinear (possibly) degenerate parabolic
systems in three cases: 1) scalar problems with confinement by a uniformly convex potential …

In this book a hierarchy of macroscopic models for semiconductor devices is presented.
Three classes of models are studied in detail: isentropic drift-diffusion equations, energy …

Global existence and long-time behavior of solutions to a family of nonlinear fourth order
evolution equations on R d are studied. These equations constitute gradient flows for the …

We prove the global existence of non-negative variational solutions to the “drift diffusion”
evolution equation\partial_t u+ div\left (u D\left (2 Δ\sqrt u\sqrt uf\right)\right)= 0 under …

A positivity-preserving numerical scheme for a strongly coupled cross-diffusion model for
two competing species is presented, based on a semi-discretization in time. The variables …

In this paper we investigate the large-time behavior of strong solutions to the one-
dimensional fourth order degenerate parabolic equation ut=−(uu xxx) x, modeling the …

We consider the quantum drift diffusion model for semiconductor devices and collect recent
results on the stationary and transient equations. The stationary model including generation …

The logarithmic fourth-order equation \partial_tu+\frac12i,j=1^dij^2(uij^2\logu)=0, called the
Derrida–Lebowitz–Speer–Spohn equation, with periodic boundary conditions is analyzed …

\noindent A positivity-preserving numerical scheme for a fourth order nonlinear parabolic
system arising in quantum semiconductor modeling is studied. The system is numerically …