Optimal lower bounds on asymptotic support propagation rates for the thin-film equation

J.L. Fischer, Journal of Differential Equations 255 (2013) 3127–3149.

Download
No fulltext has been uploaded. References only!

Journal Article | Published
Abstract
We derive lower bounds on asymptotic support propagation rates for strong solutions of the Cauchy problem for the thin-film equation. The bounds coincide up to a constant factor with the previously known upper bounds and thus are sharp. Our results hold in case of at most three spatial dimensions and n∈. (1, 2.92). The result is established using weighted backward entropy inequalities with singular weight functions to yield a differential inequality; combined with some entropy production estimates, the optimal rate of propagation is obtained. To the best of our knowledge, these are the first lower bounds on asymptotic support propagation rates for higher-order nonnegativity-preserving parabolic equations.
Publishing Year
Date Published
2013-11-15
Journal Title
Journal of Differential Equations
Volume
255
Issue
10
Page
3127 - 3149
IST-REx-ID

Cite this

Fischer JL. Optimal lower bounds on asymptotic support propagation rates for the thin-film equation. Journal of Differential Equations. 2013;255(10):3127-3149. doi:10.1016/j.jde.2013.07.028
Fischer, J. L. (2013). Optimal lower bounds on asymptotic support propagation rates for the thin-film equation. Journal of Differential Equations, 255(10), 3127–3149. https://doi.org/10.1016/j.jde.2013.07.028
Fischer, Julian L. “Optimal Lower Bounds on Asymptotic Support Propagation Rates for the Thin-Film Equation.” Journal of Differential Equations 255, no. 10 (2013): 3127–49. https://doi.org/10.1016/j.jde.2013.07.028.
J. L. Fischer, “Optimal lower bounds on asymptotic support propagation rates for the thin-film equation,” Journal of Differential Equations, vol. 255, no. 10, pp. 3127–3149, 2013.
Fischer JL. 2013. Optimal lower bounds on asymptotic support propagation rates for the thin-film equation. Journal of Differential Equations. 255(10), 3127–3149.
Fischer, Julian L. “Optimal Lower Bounds on Asymptotic Support Propagation Rates for the Thin-Film Equation.” Journal of Differential Equations, vol. 255, no. 10, Academic Press, 2013, pp. 3127–49, doi:10.1016/j.jde.2013.07.028.

Export

Marked Publications

Open Data IST Research Explorer

Search this title in

Google Scholar