51. Uniform formula for the riemann solutions of a scalar combustion model
- Author
-
Xiaozhou Yang, Chunlong Yang, and Gaowei Cao
- Subjects
Physics ,Geometric function theory ,Astrophysics::High Energy Astrophysical Phenomena ,General Mathematics ,Riemann surface ,010102 general mathematics ,Mathematical analysis ,Detonation ,General Physics and Astronomy ,Riemann's differential equation ,Nonlinear Sciences::Cellular Automata and Lattice Gases ,01 natural sciences ,010101 applied mathematics ,Theoretical physics ,Riemann hypothesis ,symbols.namesake ,Riemann problem ,Riemann sum ,symbols ,Deflagration ,0101 mathematics - Abstract
In this paper, we construct a uniform formula for the Riemann solutions of the simplified Chapman-Jouguet model. Firstly, we define a new functional, and then, we obtain that the Riemann solutions can be expressed by the maximum value point of this functional, while Riemann solutions may contain some of strong detonation waves, Chapman-Jouguet detonation waves and contact discontinuities. Finally, Chapman-Jouguet deflagration waves are also discussed.
- Published
- 2016