---
_id: '1309'
abstract:
- lang: eng
text: We show that weak solutions of the Derrida-Lebowitz-Speer-Spohn (DLSS) equation
display infinite speed of support propagation. We apply our method to the case
of the quantum drift-diffusion equation which augments the DLSS equation with
a drift term and possibly a second-order diffusion term. The proof is accomplished
using weighted entropy estimates, Hardy's inequality and a family of singular
weight functions to derive a differential inequality; the differential inequality
shows exponential growth of the weighted entropy, with the growth constant blowing
up very fast as the singularity of the weight becomes sharper. To the best of
our knowledge, this is the first example of a nonnegativity-preserving higher-order
parabolic equation displaying infinite speed of support propagation.
author:
- first_name: Julian L
full_name: Julian Fischer
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
citation:
ama: Fischer JL. Infinite speed of support propagation for the Derrida-Lebowitz-Speer-Spohn
equation and quantum drift-diffusion models. Nonlinear Differential Equations
and Applications. 2014;21(1):27-50. doi:10.1007/s00030-013-0235-0
apa: Fischer, J. L. (2014). Infinite speed of support propagation for the Derrida-Lebowitz-Speer-Spohn
equation and quantum drift-diffusion models. Nonlinear Differential Equations
and Applications. Birkhäuser. https://doi.org/10.1007/s00030-013-0235-0
chicago: Fischer, Julian L. “Infinite Speed of Support Propagation for the Derrida-Lebowitz-Speer-Spohn
Equation and Quantum Drift-Diffusion Models.” Nonlinear Differential Equations
and Applications. Birkhäuser, 2014. https://doi.org/10.1007/s00030-013-0235-0.
ieee: J. L. Fischer, “Infinite speed of support propagation for the Derrida-Lebowitz-Speer-Spohn
equation and quantum drift-diffusion models,” Nonlinear Differential Equations
and Applications, vol. 21, no. 1. Birkhäuser, pp. 27–50, 2014.
ista: Fischer JL. 2014. Infinite speed of support propagation for the Derrida-Lebowitz-Speer-Spohn
equation and quantum drift-diffusion models. Nonlinear Differential Equations
and Applications. 21(1), 27–50.
mla: Fischer, Julian L. “Infinite Speed of Support Propagation for the Derrida-Lebowitz-Speer-Spohn
Equation and Quantum Drift-Diffusion Models.” Nonlinear Differential Equations
and Applications, vol. 21, no. 1, Birkhäuser, 2014, pp. 27–50, doi:10.1007/s00030-013-0235-0.
short: J.L. Fischer, Nonlinear Differential Equations and Applications 21 (2014)
27–50.
date_created: 2018-12-11T11:51:17Z
date_published: 2014-01-01T00:00:00Z
date_updated: 2021-01-12T06:49:47Z
day: '01'
doi: 10.1007/s00030-013-0235-0
extern: 1
intvolume: ' 21'
issue: '1'
month: '01'
page: 27 - 50
publication: Nonlinear Differential Equations and Applications
publication_status: published
publisher: Birkhäuser
publist_id: '5960'
quality_controlled: 0
status: public
title: Infinite speed of support propagation for the Derrida-Lebowitz-Speer-Spohn
equation and quantum drift-diffusion models
type: journal_article
volume: 21
year: '2014'
...