CRITICAL EXPONENTS FOR THE BLOWUP OF SOLUTIONS WITH SIGN CHANGES IN ASEMILINEAR PARABOLIC EQUATION, II

The blowup of solutions of the Cauchy problem [GRAPHICS] is studied. L et Lambda(k) be the set of functions on R which change sign k times. I t is shown that for p(k) = 1 1 + 2/(k + 1), k = 0, 1, 2, ..., any solu tion with u(0) is an element of Lambda(k) blows up in finite lime if 1 < p less than or equal to p(k), whereas a global solution with u(0) i s an element of Lambda(k) exists if p > p(k). This is an extension of our previous result [17], in which a fast decay condition was imposed on initial data. It is also shown in this paper that if u, decays more slowly than \x\(-2/(p-1)) as \x\ --> + infinity, then the solution bl ows up in finite time regardless of the number of sign changes. (C) 19 98 Academic Press.