Abstract
We investigate the large time behavior for the inhomogeneous damped wave equation with nonlinear memory phi(tt)(t,omega)-Delta phi(t,omega)+phi(t)(t,omega) = 1/Gamma(1-rho)integral(t)(0)(t - sigma)(-rho)vertical bar phi(sigma, omega)vertical bar(q)d sigma + mu(omega), t > 0, omega is an element of R-N imposing the condition (phi(0, omega), phi(t)(0, omega)) = (phi(0)(omega), phi(1)(omega)) in R-N, where N >= 1, q > 1, 0 < rho < 1, phi(i) is an element of L-loc(1)(R-N), i = 0, 1, mu is an element of L-loc(1)(R-N) and mu not equivalent to 0. Namely, it is shown that, if phi(0), phi(1) >= 0, mu is an element of L-1(R-N) and integral(RN)mu(omega)d omega > 0, then for all q > 1, the considered problem has no global weak solution.