We consider a physical model of straight flame front propagation in a homogeneous solid medium in one space dimension governed by a free boundary problem. The position of the flame front at time t is  and  is the temperature at time t in the domain bounded by the front. We are particularly interested in the evolution over time of the pair  We define a notion of traveling wave solution or stationary wave solution, the couple  with  a front propagation velocity and  a stationary temperature. We show that the solution of our problem converges to a wave solution when  Finally, the theoretical results are confirmed by various numerical tests.

free boundary problem, heat equation, traveling wave solution, Laplace transform, asymptotic behavior.

Received: November 6, 2024; Revised: December 4, 2024; Accepted: December 14, 2024; Published: December 19, 2024

How to cite this article: Mohamed KARIMOU GAZIBO and Aboubacar ABDOU, Asymptotic behavior of a front propagation model: case of a one-dimensional free boundary problem, International Journal of Numerical Methods and Applications 25(1) (2025), 63-85. https://doi.org/10.17654/0975045225003

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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