Wave equations with time-dependent dissipation I. Non-effective dissipation

Abstract

The goal of this article is to construct structural representations of the solutions to Cauchy problems for weakly dissipative wave equations below scaling and to deduce estimates of the solution and its energy based on Lq (ℝn), q ≥ 2. Furthermore, the sharpness of the obtained estimates is discussed. © 2005 Elsevier Inc. All rights reserved.