S. Filippas et F. Merle, MODULATION THEORY FOR THE BLOWUP OF VECTOR-VALUED NONLINEAR HEAT-EQUATIONS, Journal of differential equations, 116(1), 1995, pp. 119-148
This paper is concerned with the blowup of solutions of the nonlinear
vector-valued heat equation U-t-Delta U=\U\(p-1) U, U(0)=U-0, where U(
x, t)=(u(1)(x, t), ..., u(m)(x, t)) is a vector-valued function from R
(n)x(0, T) to R(m) and 1 < p < (3n + 8)/(3n - 4). Working with the equ
ation in similarity variables, and using modulation theory and ideas f
rom center manifold theory, we obtain the asymptotic behavior of U in
a backward space-time parabola near any blowup point. (C) 1995 Academi
c Press, Inc.