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 to the linear equation □u+u_t=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+u_t=|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).