We consider, an initial-value problem for the thermal-diffusive combustion system
where , , , , , with , is an even nonnegative integer, and the initial data , are bounded uniformly continuous and nonnegative. It is known that by a simple comparison if , , and with , the solutions are uniformly bounded in time. When , , with , Collet and Xin  proved the existence of global classical solutions and showed that the norm of can not grow faster than for any space dimension. In our case, no comparison principle seems to apply. Nevertheless using techniques form , we essentially prove the existence of global classical solutions if , , and .
Submitted December 5, 2001. Published August 19, 2002.
Math Subject Classifications: 35B40, 35B45, 35K55, 35K65.
Key Words: Reaction-diffusion systems, positivity, global existence, boundedness.
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|Salah Badraoui |
Universite du 8 Mai 1945-Guelma,
Faculte des Sciences et Technologie,
BP.401, Guelma 24000, Algeria
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