Large time asymptotics for a class of wave equations of higher order with a variable coefficient and time‐independent incitation
Matthias Winter · Mathematical Methods in the Applied Sciences · 1995
Abstract We consider the equation (−1)m∇m (p∇mu) + ∂ u = ƒ in ℝn × [0, ∞] for arbitrary positive integers m and n and under the assumptions p −1, ƒ ϵ 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.