Multi-dimensional combustion waves for Lewis number close to one

This paper is devoted to the study of multi-dimensional travelling wave solution for a thermo-diffusive model, describing the propagation of curved flames in an infinite cylinder. The linear dependence of the components of the reaction rate together with the existence of an ignition temperature ensure that the corresponding linearized operator does not satisfy the Fredholm property. A direct consequence is that solvability conditions for the linearized operator are not known and classical methods of nonlinear analysis cannot be directly applied. We prove in this paper existence results of such travelling waves, by first introducing a suitable re-formulation of the equations and then by choosing suitable weighted spaces that allows us to move the essential spectrum away from zero.