Sensitivity analysis of 1-d steady forced scalar conservation laws
Ersoy M, Feireisl E, Zuazua E (2013)
Publication Type: Journal article
Publication year: 2013
Journal
Book Volume: 254
Pages Range: 3817-3834
Journal Issue: 9
DOI: 10.1016/j.jde.2013.01.041
Abstract
We analyze 1 - d forced steady state scalar conservation laws. We first show the existence and uniqueness of entropy solutions as limits as t -> infinity of the corresponding solutions of the scalar evolutionary hyperbolic conservation law. We then linearize the steady state equation with respect to perturbations of the forcing term. This leads to a linear first order differential equation with, possibly, discontinuous coefficients. We show the existence and uniqueness of solutions in the context of duality solutions. We also show that this system corresponds to the steady state version of the linearized evolutionary hyperbolic conservation law. This analysis leads us to the study of the sensitivity of the shock location with respect to variations of the forcing term, an issue that is relevant in applications to optimal control and parameter identification problems. (C) 2013 Elsevier Inc. All rights reserved.
Authors with CRIS profile
Involved external institutions
Basque Center of Applied Mathematics (BCAM)
Spain (ES)
Academy of Sciences of the Czech Republic (ASCR) / Akademie věd České republiky (AVČR)
Czech Republic (CZ)
Spain (ES)
Academy of Sciences of the Czech Republic (ASCR) / Akademie věd České republiky (AVČR)
Czech Republic (CZ)
How to cite
APA:
Ersoy, M., Feireisl, E., & Zuazua, E. (2013). Sensitivity analysis of 1-d steady forced scalar conservation laws. Journal of Differential Equations, 254(9), 3817-3834. https://dx.doi.org/10.1016/j.jde.2013.01.041
MLA:
Ersoy, Mehmet, Eduard Feireisl, and Enrique Zuazua. "Sensitivity analysis of 1-d steady forced scalar conservation laws." Journal of Differential Equations 254.9 (2013): 3817-3834.
BibTeX: Download