Weakly nonlinear asymptotics of the kappa-theta model for cellular flames: the Q-S equation.

We consider a quasi-steady version of the κ-θ model of flame front dynamics introduced in [FGS03]. In this case the mathematical model reduces to a single integro-differential equation. We show that a periodic problem for the latter equation is globally well-posed in Sobolev spaces of periodic functions. We prove that near the instability threshold the solutions of the equation are arbitrarily close to these of the Kuramoto–Sivashinsky equation...