On blow-up rate for sign-changing solutions in a convex domain

摘要

This paper studies a growth rate of a solution blowing up at time T of the semilinear heat equation u(t) - Deltau - u(p-1)u=0 in a convex domain D in R-n with zero-boundary condition. For a subcritical. p is an element of (1,(n+2)/(n-2)) a growth rate estimate u(x,t) less than or equal to C(T-t)(-1/(p-1)), x is an element of D, t is an element of (0, T) is established with C independent of t provided that D is uniformly C-2. The estimate applies to sign-changing solutions. The same estimate has been recently established when D = R-n by authors. The proof is similar but we need to establish L-h - L-k estimate for a time-dependent domain because of the presence of the boundary. Copyright (C) 2004 John Wiley Sons, Ltd.