Abstract Structure-preserving numerical schemes for a nonlinear parabolic fourth-order
equation, modeling the electron transport in quantum semiconductors, with periodic …

We prove uniqueness of solutions of the DLSS equation in a class of sufficiently regular
functions. The global weak solutions of the DLSS equation constructed by Jüngel and …

New one‐leg multistep time discretizations of nonlinear evolution equations are
investigated. The main features of the scheme are the preservation of the non‐negativity and …

We propose a spatial discretization of the fourth-order nonlinear DLSS equation on the
circle. Our choice of discretization is motivated by a novel gradient flow formulation with …

A nonlinear parabolic equation of sixth order is analyzed. The equation arises as a reduction
of a model from quantum statistical mechanics and also as the gradient flow of a second …

We establish sharp criteria for the instantaneous propagation of free boundaries in solutions
to the thin-film equation. The criteria are formulated in terms of the initial distribution of mass …

In this paper, we deal with two logarithmic fourth order differential equations: the extended
one-dimensional DLSS equation and its multi-dimensional analog. We show the global …

In this paper we construct a unique global in time weak nonnegative solution to the
corrected Derrida-Lebowitz-Speer-Spohn equation, which statistically describes the …

A degenerate fourth-order parabolic equation modeling condensation phenomena related to
Bose–Einstein particles is analyzed. The model is a Fokker–Planck-type approximation of …

We present an algorithm for the derivation of lower bounds on support propagation for a
certain class of nonlinear parabolic equations. We proceed by combining the ideas in some …