# American Institute of Mathematical Sciences

October  2010, 14(3): 817-869. doi: 10.3934/dcdsb.2010.14.817

## Existence of pulsating waves in a monostable reaction-diffusion system in solid combustion

 1 Institut de Mathématiques (UMR CNRS 5219), Université Paul Sabatier, 31062 Toulouse Cedex 4, France, France

Received  August 2008 Revised  April 2010 Published  July 2010

In this paper, we study the solid combustion system with the monostable nonlinearity $f(T)=T$. Our goal is to prove the existence of pulsating waves.
First, the specific form of the nonlinearity leads to transform the problem into a scalar reaction diffusion equation with nonusual infinite limits.
Next, we prove that this scalar equation admits a family of pulsating waves, applying an easy fixed point argument; moreover we precise the asymptotic behaviour of the pulsating waves, developping them in Fourier series and studying the behaviour of its Fourier coefficients.
Finally, all these informations on the equation let us prove that there exists a family of pulsating waves of the original SHS system, the family of admissible propagation speed being a precised half-line.
Citation: Michaël Bages, Patrick Martinez. Existence of pulsating waves in a monostable reaction-diffusion system in solid combustion. Discrete and Continuous Dynamical Systems - B, 2010, 14 (3) : 817-869. doi: 10.3934/dcdsb.2010.14.817
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