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Rate of Type II blowup for a semilinear heat equation

Authors:

Noriko Mizoguchi

Affiliation:

(1) Department of Mathematics, Tokyo Gakugei University, Koganei, Tokyo 184-8501, Japan

Abstract:

A solution u of a Cauchy problem for a semilinear heat equation

$left{ begin{array}{ll}u_{t} = Delta u + u^{p} & quad {rm in}, {bf R}^N times (0,,T),u(x,0) = u_{0}(x) geq 0 & quad {rm in}, {bf R}^N end{array} right.$

is said to undergo Type II blowup at t = T if lim sup $_{t nearrow T} ; (T-t)^{1/(p-1)} |u(t)|_infty = infty .$ Let $$varphi_infty$$

be the radially symmetric singular steady state. Suppose that $$u_0 in L^infty$$

is a radially symmetric function such that $$u_0 - varphi_infty$$

and (u ₀)_t change sign at most finitely many times. We determine the exact blowup rate of Type II blowup solution with initial data u ₀ in the case of p > p _L, where p _L is the Lepin exponent.

Keywords:

KeywordHeading" >Mathematics Subject Classification (2000) 35K20 35K55 58K57

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