(Bounded) Traveling combustion fronts with degenerate kinetics

Abstract We consider the propagation of a flame front in a solid periodic medium. It is governed by an equation of Hamilton–Jacobi type, whose front’s velocity depends on the temperature via a nonlinear degenerate kinetic rate. The temperature solves a free boundary problem subject to boundary conditions depending on the front’s velocity itself. We show the existence of nonplanar traveling wave solutions which are bounded and global. Previous results by the same authors (cf. Alibaud and Namah, 2017) were obtained for essentially positively lower bounded kinetics or eventually which have some very weak degeneracy. Here we consider very general degenerate kinetics, including for the first tim…