Global existence of solution of Cauchy problem for a non-linear wave equation.

In this paper, we prove that the Cauchy problem for a non-linear wave equation (1)has a unique global generalized solutions in and a unique global classical solution in . We also prove that the Cauchy problem for the equation (1) admits a unique global generalized solution in C2([0, ∞); Wm, p(R) ∩ L∞(R))(m ≥ 0 is an integer,1 ≤ p ≤ ∞) and a unique global classical solution in . [ABSTRACT FROM AUTHOR]