Study of a Model Equation in Detonation Theory

Handle URI:
http://hdl.handle.net/10754/555743
Title:
Study of a Model Equation in Detonation Theory
Authors:
Faria, Luiz ( 0000-0001-8159-4442 ) ; Kasimov, Aslan R.; Rosales, Rodolfo R.
Abstract:
Here we analyze properties of an equation that we previously proposed to model the dynamics of unstable detonation waves [A. R. Kasimov, L. M. Faria, and R. R. Rosales, Model for shock wave chaos, Phys. Rev. Lett., 110 (2013), 104104]. The equation is ut+ 1/2 (u2-uu (0-, t))x=f (x, u (0-, t)), x > 0, t < 0. It describes a detonation shock at x = 0 with the reaction zone in x > 0. We investigate the nature of the steady-state solutions of this nonlocal hyperbolic balance law, the linear stability of these solutions, and the nonlinear dynamics. We establish the existence of instability followed by a cascade of period-doubling bifurcations leading to chaos. © 2014 Society for Industrial and Applied Mathematics.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Citation:
Study of a Model Equation in Detonation Theory 2014, 74 (2):547 SIAM Journal on Applied Mathematics
Journal:
SIAM Journal on Applied Mathematics
Issue Date:
24-Apr-2014
DOI:
10.1137/130938232
Type:
Article
ISSN:
0036-1399; 1095-712X
Additional Links:
http://epubs.siam.org/doi/abs/10.1137/130938232; http://arxiv.org/abs/1407.8466
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorFaria, Luizen
dc.contributor.authorKasimov, Aslan R.en
dc.contributor.authorRosales, Rodolfo R.en
dc.date.accessioned2015-05-26T06:59:31Zen
dc.date.available2015-05-26T06:59:31Zen
dc.date.issued2014-04-24en
dc.identifier.citationStudy of a Model Equation in Detonation Theory 2014, 74 (2):547 SIAM Journal on Applied Mathematicsen
dc.identifier.issn0036-1399en
dc.identifier.issn1095-712Xen
dc.identifier.doi10.1137/130938232en
dc.identifier.urihttp://hdl.handle.net/10754/555743en
dc.description.abstractHere we analyze properties of an equation that we previously proposed to model the dynamics of unstable detonation waves [A. R. Kasimov, L. M. Faria, and R. R. Rosales, Model for shock wave chaos, Phys. Rev. Lett., 110 (2013), 104104]. The equation is ut+ 1/2 (u2-uu (0-, t))x=f (x, u (0-, t)), x > 0, t < 0. It describes a detonation shock at x = 0 with the reaction zone in x > 0. We investigate the nature of the steady-state solutions of this nonlocal hyperbolic balance law, the linear stability of these solutions, and the nonlinear dynamics. We establish the existence of instability followed by a cascade of period-doubling bifurcations leading to chaos. © 2014 Society for Industrial and Applied Mathematics.en
dc.relation.urlhttp://epubs.siam.org/doi/abs/10.1137/130938232en
dc.relation.urlhttp://arxiv.org/abs/1407.8466en
dc.rightsArchived with thanks to SIAM Journal on Applied Mathematicsen
dc.subjectdetonation instabilityen
dc.subjectchaosen
dc.subjectshock waveen
dc.titleStudy of a Model Equation in Detonation Theoryen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalSIAM Journal on Applied Mathematicsen
dc.eprint.versionPublisher's Version/PDFen
dc.contributor.institutionDepartment of Mathematics, MIT, Cambridge, MA 02139en
dc.identifier.arxividarXiv:1407.8466en
kaust.authorFaria, Luizen
kaust.authorKasimov, Aslan R.en
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