Global Existence of Solutions of Volterra Integrodifferential Equations of Parabolic Type

Sufficient conditions for the global existence of a strong solution of the equation ut (t, x) = ∫t0k(t − s) σ(ux(s, x))xds + f(t, x) are given. The kernel k satisfies (z) ≥ κ (z) and σ is increasing with sup {σ′ (p) } < 1 + 2κ([formula] + κ).