On Majda's model for dynamic combustion

Journal Article · Wed Jan 01 04:00:00 EST 1992 · Communications in Partial Differential Equations; (United States)

DOI:https://doi.org/10.1080/03605309208820858· OSTI ID:7164071

Levy, A ^[1]

---

1. Hebrew Univ., Jerusalem (Israel)

Majda's model of dynamic combustion, consists of the system, (u [plus] q[sub 0]z)[sub t] [plus] f(u)[sub x] = 0, z[sub t] [plus] K[rho](u)z = 0. In this paper the Cauchy problem is considered. A weak entropy solution for this system is defined, existence, uniqueness and continuous dependence on initial data are proved, as well as finite propagation speed, for initial data in L[infinity]. The existence is proved via the 'vanishing viscosity method' . Furthermore it is proved that the solution to the Riemann problem converges as t [yields] [infinity] to the Z-N-D traveling wave solution. In the appendices, a second order numerical scheme for the model is described, and some numerical results are presented.

• OSTI ID: 7164071
• Journal Information: Communications in Partial Differential Equations; (United States), Journal Name: Communications in Partial Differential Equations; (United States) Vol. 17:3 and 4; ISSN 0360-5302; ISSN CPDIDZ
• Country of Publication: United States
• Language: English

Related Subjects

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
400800* -- Combustion
Pyrolysis
& High-Temperature Chemistry
CAUCHY PROBLEM
CHEMICAL REACTION KINETICS
CHEMICAL REACTIONS
COMBUSTION KINETICS
CONVERGENCE
DYNAMICS
FLUID MECHANICS
FUNCTIONS
KINETICS
MATHEMATICAL MODELS
MECHANICS
NUMERICAL SOLUTION
REACTION KINETICS
RIEMANN FUNCTION