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

摘要

AbstractWe consider the equation (−1)m∇m(p∇mu) + ∂ t2u= ƒ in ℝn× 0, ∞ for arbitrary positive integersmandnand under the assumptionsp−1, ƒ ϵC 0∞andp>0. Under the additional assumption that the differential operator (−1)m∇m(p∇mu) has no eigenvalues we derive an asymptotic expansion foru(x,t) ast→ including all terms up to ordero(1). In particular, we show that for 2m≥nterms of the orderstα, logt,