Abstract: | Let Ω be a domain in ?n and let m? ?; be given. We study the initial-boundary value problem for the equation with a homogeneous Dirichlet boundary condition; here u is a scalar function, $ \bar D_x^m u: = (\partial _x^\alpha u)_{|\alpha | \le m} $ and certain restrictions are made on F guaranteeing that energy estimates are possible. We prove the existence of a value of T>0 such that a unique classical solution u exists on 0, T]×Ω. Furthermore, we show that T → ∞ if the data tend to zero. |