Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Remote Access
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On the detonation of a combustible gas


Author: Robert A. Gardner
Journal: Trans. Amer. Math. Soc. 277 (1983), 431-468
MSC: Primary 35L67; Secondary 58E07, 76L05
MathSciNet review: 694370
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: This paper is concerned with the existence of detonation waves for a combustible gas. The equations are those of a viscous, heat conducting, polytropic gas coupled with an additional equation which governs the evolution of the mass fraction of the unburned gas (see (1)). The reaction is assumed to be of the simplest form: $ A \to B$, i.e., there is a single product and a single reactant. The main result (see Theorem 2.1) is a rigorous existence theorem for strong, and under certain conditions, weak detonation waves for explicit ranges of the viscosity, heat conduction, and species diffusion coefficients. In other words, a class of admissible "viscosity matrices" is determined.

The problem reduces to finding an orbit of an associated system of four ordinary differential equations which connects two distinct critical points. The proof employs topological methods, including Conley's index of isolated invariant sets.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 35L67, 58E07, 76L05

Retrieve articles in all journals with MSC: 35L67, 58E07, 76L05


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1983-0694370-1
PII: S 0002-9947(1983)0694370-1
Article copyright: © Copyright 1983 American Mathematical Society



Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia