Abstract: | We consider the equation (?1)m?m (p?mu) + ? u = ? in ?n × 0, ∞] for arbitrary positive integers m and n and under the assumptions p ?1, ? ? C and p > 0. Under the additional assumption that the differential operator (?1)m?m (p?mu) has no eigenvalues we derive an asymptotic expansion for u(x,t) as t → including all terms up to order o(1). In particular, we show that for 2m ≥ n terms of the orders tα, log t, (log t)2 and tβ·log t as t → ∞ may occur. |