About: Sensitivity analysis of 1d steady forced scalar conservation laws

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	We analyze 1d forced steady state scalar conservation laws. We first show the existence and uniqueness of entropy solutions as limits as t tends to 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. We analyze 1d forced steady state scalar conservation laws. We first show the existence and uniqueness of entropy solutions as limits as t tends to 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. (en)
Title	Sensitivity analysis of 1d steady forced scalar conservation laws Sensitivity analysis of 1d steady forced scalar conservation laws (en)
skos:prefLabel	Sensitivity analysis of 1d steady forced scalar conservation laws Sensitivity analysis of 1d steady forced scalar conservation laws (en)
skos:notation	RIV/67985840:_____/13:00391347!RIV14-GA0-67985840
http://linked.open...avai/predkladatel	Matematický ústav AV ČR, v. v. i.
http://linked.open...avai/riv/aktivita	I P
http://linked.open...avai/riv/aktivity	I, P(GA201/09/0917)
http://linked.open...iv/cisloPeriodika	9
http://linked.open...vai/riv/dodaniDat	2014
http://linked.open...aciTvurceVysledku	Feireisl, Eduard
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Matematický ústav AV ČR, v. v. i.
http://linked.open...dnocenehoVysledku	104668
http://linked.open...ai/riv/idVysledku	RIV/67985840:_____/13:00391347
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	sensitivity; scalar conservation law; control (en)
http://linked.open.../riv/klicoveSlovo	scalar conservation law control sensitivity
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[26EC620824F6]
http://linked.open...i/riv/nazevZdroje	Journal of Differential Equations
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	3 (xsd:int)
http://linked.open...vavai/riv/projekt	Mathematical and computer analysis of the evolution processes in nonlinear viscoelastic fluid-like materials
http://linked.open...UplatneniVysledku	2013
http://linked.open...v/svazekPeriodika	254
http://linked.open...iv/tvurceVysledku	Feireisl, Eduard Zuazua, E. Ersoy, M.
http://linked.open...ain/vavai/riv/wos	000316512200007
issn	0022-0396
number of pages	18 (xsd:int)
http://bibframe.org/vocab/doi	10.1016/j.jde.2013.01.041

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