A critical exponent in a degenerate parabolic equation

We consider positive solutions of the Cauchy problem in $mathbb{R,}^n$ for the equation $$u_t=u^p,Delta u+u^q,quad pgeq1,; qgeq 1$$nopagenumbersend and show that concerning global solvability, the number q = p + 1 appears as a critical growth exponent. Copyright © 2002 John Wiley & Sons, Ltd.