Study of a Model Equation in Detonation Theory
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 $ u_{t}+\tfrac{1}{2}\left(u^{2}-uu\left(0^{-},t\...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
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Society for Industrial and Applied Mathematics
2014
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| Online Access: | http://hdl.handle.net/1721.1/89464 https://orcid.org/0000-0002-8828-5930 |
| _version_ | 1826202123626348544 |
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| author | Faria, Luiz M. Kasimov, Aslan R. Rosales, Rodolfo R. |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Faria, Luiz M. Kasimov, Aslan R. Rosales, Rodolfo R. |
| author_sort | Faria, Luiz M. |
| collection | MIT |
| description | 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 $ u_{t}+\tfrac{1}{2}\left(u^{2}-uu\left(0^{-},t\right)\right)_{x}=f\left(x,u\left(0^{-},t\right)\right),\;x\le0,\; 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. |
| first_indexed | 2024-09-23T12:02:14Z |
| format | Article |
| id | mit-1721.1/89464 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T12:02:14Z |
| publishDate | 2014 |
| publisher | Society for Industrial and Applied Mathematics |
| record_format | dspace |
| spelling | mit-1721.1/894642022-10-01T07:44:21Z Study of a Model Equation in Detonation Theory Faria, Luiz M. Kasimov, Aslan R. Rosales, Rodolfo R. Massachusetts Institute of Technology. Department of Mathematics Rosales, Rodolfo R. 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 $ u_{t}+\tfrac{1}{2}\left(u^{2}-uu\left(0^{-},t\right)\right)_{x}=f\left(x,u\left(0^{-},t\right)\right),\;x\le0,\; 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. National Science Foundation (U.S.) (Grant DMS-1115278) National Science Foundation (U.S.) (Grant DMS-1007967) National Institutes of Health (U.S.) (grant DMS-0907955) 2014-09-12T16:50:28Z 2014-09-12T16:50:28Z 2014-04 2014-01 Article http://purl.org/eprint/type/JournalArticle 0036-1399 1095-712X http://hdl.handle.net/1721.1/89464 Faria, Luiz M., Aslan R. Kasimov, and Rodolfo R. Rosales. “Study of a Model Equation in Detonation Theory.” SIAM Journal on Applied Mathematics 74, no. 2 (April 24, 2014): 547–570. © 2014, Society for Industrial and Applied Mathematics. https://orcid.org/0000-0002-8828-5930 en_US http://dx.doi.org/10.1137/130938232 SIAM Journal on Applied Mathematics Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf Society for Industrial and Applied Mathematics Society for Industrial and Applied Mathematics |
| spellingShingle | Faria, Luiz M. Kasimov, Aslan R. Rosales, Rodolfo R. Study of a Model Equation in Detonation Theory |
| title | Study of a Model Equation in Detonation Theory |
| title_full | Study of a Model Equation in Detonation Theory |
| title_fullStr | Study of a Model Equation in Detonation Theory |
| title_full_unstemmed | Study of a Model Equation in Detonation Theory |
| title_short | Study of a Model Equation in Detonation Theory |
| title_sort | study of a model equation in detonation theory |
| url | http://hdl.handle.net/1721.1/89464 https://orcid.org/0000-0002-8828-5930 |
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