Improved decay rates for solutions to one-dimensional linear and semilinear dissipative wave equations in all space

Better decay estimates to the 1-dimensional Cauchy problem on R to the linear equation ✷u + ut = 0 can be discussed under rather restricted conditions on the initial data. Furthermore, as applications we derive the small data global existence result to the equation ✷u + ut = |u|p−1u, which has the “odd” functions as the initial data. Furthermore, the new method (see R. Ikehata, T. Matsuyama, Sci.Math. Japon. 55 (2002) 33–42) used in the first half will be applied to the problem coming from Ehrenpreis (Sugaku 26 (1974) 168).  2003 Elsevier Science (USA). All rights reserved.