A Cacciopoli-Type Inequality to Prove Coercivity of a Bilinear Form Associated with Spatial Hysteresis Internal Damping for an Euler-Bernoulli Beam

Authors

Bernd S.W. Schröder, University of Southern Mississippi
Jonathan B. Walters, Louisiana Tech University
Katie A. Evans, Louisiana Tech University

Document Type

Article

Publication Date

2016

Department

Mathematics

School

Mathematics and Natural Sciences

Abstract

We prove an inequality that resembles Cacciopoli inequalities in that it bounds the norm of the derivative of a function by using the norm of the function. Unlike in Cacciopoli inequalities, there is no restriction on the function, a fact made up for by adding an extra term to the norm of the function. The inequality arose in the proof that a bilinear form associated with spatial hysteresis internal damping for an Euler-Bernoulli beam is coercive.

Comments

© 2016. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/.

Publication Title

Journal of Mathematical Analysis and Applications

Volume

425

Issue

1

First Page

520

Last Page

535

Recommended Citation

Schröder, B. S., Walters, J. B., Evans, K. A. (2016). A Cacciopoli-Type Inequality to Prove Coercivity of a Bilinear Form Associated with Spatial Hysteresis Internal Damping for an Euler-Bernoulli Beam. Journal of Mathematical Analysis and Applications, 425(1), 520-535.
Available at: https://aquila.usm.edu/fac_pubs/15691