Global Large Time Self-similarity of a Thermal-diiusive Combustion System with Critical Nonlinearity

@inproceedings{Bricmont1995GlobalLT,
  title={Global Large Time Self-similarity of a Thermal-diiusive Combustion System with Critical Nonlinearity},
  author={Jean Bricmont and Antti Kupiainen and Jack Xin},
  year={1995}
}
We study the initial value problem of the thermal-diiusive combustion system: for non-negative spatially decaying initial data of arbitrary size and for any positive constant d. We show that if the initial data decays to zero suuciently fast at innnity, then the solution (u 1 ; u 2) converges to a self-similar solution of the reduced system: u 1;t = u 1;xx ?u 1 u 2 2 ; u 2;t = du 2;xx , in the large time limit. In particular, u 1 decays to zero like O(t ? 1 2 ?), where > 0 is an anomalous… CONTINUE READING