I will talk about several results obtained jointly with A. Bonnet and R. Monneau, on the mathematical modelling of conical shaped premixed Bunsen flames. In the simple framework of the thermodiffusive model with unit Lewis number and simple chemistry, the mathematical problem can boil down to a single advection-reaction-diffusion equation for the temperature. We have analyzed the conical shape of the bidimensional premixed flames and made rigorous the relationship between the speed of the nonplanar flame and its angle. Such a simple model enables to capture well-known physical facts; for instance, the tip of the flame cannot point in the direction opposite to the flow. We have also considered the flame front in the limit of high activation energy and we have obtained some existence and uniqueness results for related Serrin type problems.
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