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Propagation of a combustion front in a striated solid medium: A homogenization analysis. (English) Zbl 0803.35009
Summary: A model problem for the propagation of a combustion front through a periodically inhomogeneous medium is posed. The existence of a steady state solution is proved, in which the front’s velocity is periodic in time. Computer simulations are carried out. Finally, through rigorous homogenization techniques, it is shown that when the wavelength of the inhomogeneity is small, the solution may be approximated by a travelling wave solution of the corresponding problem for a medium with certain constant properties.

MSC:
35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
35K10 Second-order parabolic equations
80A25 Combustion
35B40 Asymptotic behavior of solutions to PDEs
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