Global existence and asymptotic behavior of small solutions for semilinear dissipative wave equations

We study the global existence and asymptotic behavior of solutions to the Cauchy problem for the semilinear dissipative wave equations : squareu + partial derivative(t)u = \u\(alpha+1), u\(t=0) = epsilonu(o) is an element of H-1 boolean AND L-1, partial derivative(t)u\(t=o) = epsilonu(1) is an element of L-2 boolean AND L-1 with a small parameter epsilon > 0. When N less than or equal to 3 and 2/N < α ≤ 2/[N - 2](+), we show the global solvability and derive the sharp rates of the solutions.