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

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  • 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.
    Mathematics Subject Classification: Primary: 35K57; Secondary: 34C11, 35B10, 35K50, 42A16.


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