MODULATION THEORY FOR THE BLOWUP OF VECTOR-VALUED NONLINEAR HEAT-EQUATIONS

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 equation in similarity variables, and using modulation theory and ideas from center manifold theory, we obtain the asymptotic behavior of U in a backward space-time parabola near any blowup point. (C) 1995 Academic Press, Inc.