Abstract
The paper investigates a class of a semilinear wave equation with time-dependent damping term (- 1 (1+t)beta Delta ut) and a nonlinearity |u|p. We will show the influence of the parameter beta in the blow-up results under some hy-pothesis on the initial data and the exponent p by using the test function method. We also study the local existence in time of mild solution in the energy space H-1(R-n) x L-2(R-n).