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Collet (Centre de Physique Th'eorique Laboratoire CNRS","submitted_at":"1994-12-05T10:59:26Z","abstract_excerpt":"We consider the initial value problem for the thermal-diffusive combustion systems of the form:\n  $u_{1,t}= Delta_{x}u_1 - u_1 u_2^m$, $u_{2,t}= d Delta_{x} u_2 + u_1 u_2^m$,\n  $x in R^{n}$, $n geq 1$, $m geq 1$, $d > 1$,\n with bounded uniformly continuous nonnegative initial data. For such initial data, solutions can be simple traveling fronts or complicated domain walls. Due to the well-known thermal-diffusive instabilities when $d$, the Lewis number, is sufficiently away from one, front solutions are potentially chaotic. 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