Abstract
We consider the system of nonlinear wave equations with nonlinear time fractional damping
{u(tt) + (-Delta)(m)u+D-C(0,t)alpha(t(alpha)vertical bar u vertical bar(q)) = vertical bar v vertical bar(p), t > 0, x is an element of R-N,
v(tt) + (-Delta)(m)v+D-C(0,t)beta (t(delta)vertical bar v vertical bar(r) = vertical bar v vertical bar(s), t > 0, x is an element of R-N, where (u, v) = (u(t, x), v(t, x)), m and N are positive natural numbers, p, q, r, s > 1, sigma, delta >=
(u(0, x), u(t)(0, x)) = (u(0)(x), u(1)(x)), x is an element of R-N,
(u(0, x), u(t)(0, x)) = (u(0)(x), u(1)(x)), x is an element of R-N,
0, 0 < alpha, beta < 1, and D-C(0,t)kappa, 0 < kappa < 1, is the Caputo fractional derivative of order kappa. Namely, sufficient criteria are derived so that the system admits no global weak solution. To the best of our knowledge, the considered system was not previously studied in the literature.