On the uniqueness of L1-continuation after blowup

This paper is concerned with the uniqueness of L1-continuation beyond blowup for a Cauchy problem of a semilinear heat equation ut = u +up in RN ×(0, T ), u(x, 0) = u0(x) 0 inRN (P) with p > 1, 0 < T ∞ and u0 ∈ L∞(RN). Here we say that u is an L1-solution of (P) if u ∈ C([0, T );L1 loc(RN)) with u ∈ L p loc(RN × (0, T )) satisfies (P) in the distributional sense. In the case of pS