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This work was part of my Ph. D. and I would like to express my gratitude to my advisor Prof. Jean-Michel Roquejoffre for fruitful, valuable discussions and constant support.International audienceThe aim of this work is to prove existence results and derive asymptotic limits for some nonlinear elliptic problems arising in flame propagation and set in unbounded cylinders. These problems are involved in the modelling of burner flames. The existence proof is a combination of topological degree arguments and estimates that are specific to the problems under consideration. We also derive some asymptotic limits for our model. We emphasize on the fact that the model under consideration is a system of reaction-diffusion equations

Existence and asymptotics of travelling waves in a thermo-diffusive model in half cylinders. Part I: Neumann boundary conditions