Temperature growth and temperature bounds in special cases of combustion models

Abstract

We consider reaction-diffusion equations coupling temperature and mass fraction in a one-step- reaction model of combustion. On a bounded domain with no-flux boundary conditions for the temperature and fixed Dirichlet boundary conditions for the mass fraction, we demonstrate non-boundedness of the temperature by establishing lower linear growth bounds to complement previously obtained upper linear growth bounds. When the spatial domain is the real line, uniform temperature bounds have previously been obtained if the Lewis number is less than or equal to one or if ignition occurs initially at both +∞ and -∞. We obtain here uniform temperature bounds in the case of ignition at (at most) one end only and if the Lewis number is greater than one, provided that an integrability condition is imposed on the initial mass fraction, i.e. the reaction tube contains only a finite amounnt of fuel.

Keywords:

• Reaction-diffusion equations
• Linear growth bounds
• Integrability condition
• Uniform bounds

Additional information

Notes on contributors

Joel D. Avrin

Mokhtar Kirane