Entropy-stable and entropy-dissipative approximations of a fourth-order quantum diffusion equation
Abstract Structure-preserving numerical schemes for a nonlinear parabolic fourth-order
equation, modeling the electron transport in quantum semiconductors, with periodic …
equation, modeling the electron transport in quantum semiconductors, with periodic …
Uniqueness of solutions of the Derrida-Lebowitz-Speer-Spohn equation and quantum drift-diffusion models
J Fischer - Communications in Partial Differential Equations, 2013 - Taylor & Francis
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 …
functions. The global weak solutions of the DLSS equation constructed by Jüngel and …
Entropy dissipative one‐leg multistep time approximations of nonlinear diffusive equations
A Jüngel, JP Milišić - Numerical methods for partial differential …, 2015 - Wiley Online Library
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 …
investigated. The main features of the scheme are the preservation of the non‐negativity and …
A structure preserving discretization for the Derrida-Lebowitz-Speer-Spohn equation based on diffusive transport
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 …
circle. Our choice of discretization is motivated by a novel gradient flow formulation with …
Gradient flow structure of a multidimensional nonlinear sixth-order quantum-diffusion equation
D Matthes, EM Rott - Pure and Applied Analysis, 2022 - msp.org
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 …
of a model from quantum statistical mechanics and also as the gradient flow of a second …
Sharp criteria for the waiting time phenomenon in solutions to the thin-film equation
N De Nitti, J Fischer - Communications in Partial Differential …, 2022 - Taylor & Francis
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 …
to the thin-film equation. The criteria are formulated in terms of the initial distribution of mass …
Global existence and exponential decay to equilibrium for DLSS-Type equations
H Bae, R Granero-Belinchón - Journal of Dynamics and Differential …, 2021 - Springer
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 …
one-dimensional DLSS equation and its multi-dimensional analog. We show the global …
Well-posedness and convergence of a numerical scheme for the corrected Derrida-Lebowitz-Speer-Spohn equation using the Hellinger distance
M Bukal - arXiv preprint arXiv:2001.02305, 2020 - arxiv.org
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 …
corrected Derrida-Lebowitz-Speer-Spohn equation, which statistically describes the …
A Degenerate Fourth-Order Parabolic Equation Modeling Bose–Einstein Condensation. Part I: Local Existence of Solutions
A Jüngel, M Winkler - Archive for Rational Mechanics and Analysis, 2015 - Springer
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 …
Bose–Einstein particles is analyzed. The model is a Fokker–Planck-type approximation of …
Estimates on front propagation for nonlinear higher-order parabolic equations: an algorithmic approach
J Fischer - Interfaces and Free Boundaries, 2015 - ems.press
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 …
certain class of nonlinear parabolic equations. We proceed by combining the ideas in some …