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Dynamics and stability of a weak detonation wave
KTH, Superseded Departments, Mathematics.
1999 (English)In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 202, no 3, 547-569 p.Article in journal (Refereed) Published
Abstract [en]

One dimensional weak detonation waves of a basic reactive shock wave model are proved to be nonlinearly stable, i.e. initially perturbed waves tend asymptotically to translated weak detonation waves. This model system was derived as the low Math number limit of the one component reactive Navier-Stokes equations by Majda and Roytburd [SIAM J. Sci. Stat. Comput. 43, 1086-1118 (1983)], and its weak detonation waves have been numerically observed as stable. The analysis shows in particular the key role of the new nonlinear dynamics of the position of the shock wave, The shock translation solves a nonlinear integral equation, obtained by Green's function techniques, and its solution is estimated by observing that the kernel can be split into a dominating convolution operator and a remainder. The inverse operator of the convolution and detailed properties of the traveling wave reduce, by monotonicity, the remainder to a small L-1 perturbation.

Place, publisher, year, edition, pages
NEW YORK: Springer-Verlag New York, 1999. Vol. 202, no 3, 547-569 p.
Keyword [en]
National Category
Natural Sciences
URN: urn:nbn:se:kth:diva-51574DOI: 10.1007/s002200050595ISI: 000080306200003OAI: diva2:464628
QC 20111214Available from: 2011-12-13 Created: 2011-12-13 Last updated: 2011-12-14Bibliographically approved

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