Holomorphic solutions of semilinear heat equations

with φ ∈ L(R), where P is a polynomial vanishing at the origin and ∆ stands for the Laplacian with respect to x. The analyticity in time of the solutions of a semilinear heat equation has been considered by many authors. For example Ōuchi [2] treated the analyticity in time of the solutions of certain initial boundary value problems with bounded continuous initial functions, which include (1) if P (u, u) is a monotone polynomial of u with real coefficients. The main aim of the present paper is to prove that the solution of (1) local in time with the initial function in L(R), 1 ≤ p 0 and T > 0 we let