Life span of solutions with large initial data in a semilinear parabolic equation

This paper is concerned with the Cauchy problem [GRAPHICS] where p > 1, lambda > 0, and phi is a bounded continuous function. It is sh own that the blowup time T(lambda) of the solution of this problem satisfie s T(lambda) = 1/p-1 \ phi \ (1-p)(infinity) lambda (1-p) + o(lambda (1-p)) as lambda --> infinity. Moreover, when the maximum of \(phi (x)\ is attaine d at one point, we determine the higher order term of T(lambda) which refle cts the pointedness of the peak of \ phi \.