--- _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' ...