Self-similar solutions and semi-linear wave equations in Besov spaces

We prove that the initial value problem for semi-linear wave equations is well-posed in the Besov space (B) over dot (Sp,infinity)(2) (R-n), where the nonlinearity is of type u(p), with p is an element of N and s(p) = n/2 - 2/p > 1/2. This allows to obtain self-similar solutions as well as to recover previous results under weaker smallness assumptions on the data. (C) 2000 Editions scientifiques et medicales Elsevier SAS.