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Life span of solutions with large initial data in a semilinear parabolic equation. (English) Zbl 0996.35006

The paper deals with the Cauchy problem for the semilinear parabolic equation

u t =Δu+|u| p-1 uin N ×(0,),u(x,0)=λϕ(x)in N ,

with p>1, λ>0 and ϕ being a bounded continuous function. The authors show that the blowup time T(λ) of the solution satisfies

T(λ)=1 p-1|ϕ| 1-p λ 1-p +o(λ 1-p )asλ·

Moreover, when the maximum of |ϕ(x)| is attained at one point, the higher-order term of Y(λ) is determined which reflects the pointedness of the peak of |ϕ|·

MSC:
35B30Dependence of solutions of PDE on initial and boundary data, parameters
35K55Nonlinear parabolic equations