Stability and uniqueness of global solutions to Euler equations with exothermic reaction. (August 2019)

• Record Type: Journal Article
• Authors: Hu, Kai
• Is Part Of: Nonlinear analysis. Volume 48(2019)
• Page Start: 362
• Page End: 382
• Publication Date: 2019-08
• Subjects: Euler equations -- Well-posedness -- Front tracking method; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2019.01.014
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: We consider the Cauchy problems of a non-strictly hyperbolic system which describes the compressible Euler fluid with exothermic reaction. The resonance and damping effect coexist in the system. Hence a Lyapunov-type functional in this paper is specially developed for balance laws, in order to analyze the flows generated by front tracking method, and to establish some local estimates in semigroup theory. Then we prove the well-posedness theorems and present the local features of global solutions.