Global Existence and Large Time Asymptotic Bounds of L ∞ Solutions of Thermal Diffusive Combustion Systems on R

@inproceedings{Xin1994GlobalEA,
  title={Global Existence and Large Time Asymptotic Bounds of L ∞ Solutions of Thermal Diffusive Combustion Systems on R},
  author={Jack Xin},
  year={1994}
}
We consider the initial value problem for the thermal-diffusive combustion systems of the form: u 1,t = ∆ x u 1 − u 1 u m 2 , u 2,t = d∆ x u 2 + u 1 u m 2 , x ∈ R n , n ≥ 1, m ≥ 1, d > 1, 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. It is… CONTINUE READING