 9529 J.Bricmont, A.Kupiainen, J. Xin
 Global Large Time Selfsimilarity of a ThermalDiffusive
Combustion System with Critical Nonlinearity
(53K, LateX)
Jan 25, 95

Abstract ,
Paper (src),
View paper
(auto. generated ps),
Index
of related papers

Abstract. We study the initial value problem of the thermaldiffusive combustion
system: $u_{1,t} = u_{1,x,x}  u_1 u^2_2, u_{2,t} = d u_{2,xx} + u_1 u^2_2,
x \in R^1$, for nonnegative spatially decaying initial data of arbitrary
size and for any positive constant $d$. We show that if the initial data
decays to zero sufficiently fast at infinity, then the solution $(u_1,u_2)$
converges to a selfsimilar solution of the reduced system: $u_{1,t} =
u_{1,xx}  u_1 u^2_2, u_{2,t} = d u_{2,xx}$, in the large time limit. In
particular, $u_1$ decays to zero like ${\cal O}(t^{\frac{1}{2}\delta})$,
where $\delta > 0$ is an anomalous exponent depending on the initial data,
and $u_2$ decays to zero with normal rate ${\cal O}(t^{\frac{1}{2}})$. The
idea of the proof is to combine the a priori estimates for the decay of
global solutions with the renormalization group (RG) method for
establishing
the selfsimilarity of the solutions in the large time limit.
 Files:
9529.tex