Large time asymptotics for a class of wave equations of higher order with a variable coefficient and time-independent incitation

✍ Scribed by Matthias Winter

• Publisher: John Wiley and Sons
• Year: 1995
• Tongue: English
• Weight: 795 KB
• Volume: 18
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/mma.1670180102

✦ Synopsis

Abstract

We consider the equation (−1)^m^∇^m^ (p∇^m^u) + ∂u = ƒ in ℝ^n^ × [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∇^m^u) 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 2__m__ ≥ n terms of the orders t^α^, log t, (log t)^2^ and t^β^·log t as t → ∞ may occur.