Nonexistence of Global Weak Solutions of a System of Nonlinear Wave Equations with Nonlinear Fractional Damping. (8th June 2020) - Jleli, Mohamed; Kirane, Mokhtar; Samet, Bessem
Abstract : We consider the system of nonlinear wave equations with nonlinear time fractional damping u t t + − Δ m u + C D 0, t α t σ u q = v p, t > 0, x ∈ ℝ N, v t t + − Δ m v + C D 0, t β t δ v r = v s, t > 0, x ∈ ℝ N, u 0, x, u t 0, x = u 0 x, u 1 x, x ∈ ℝ N, u 0, x, u t 0, x = u 0 x, u 1 x, x ∈ ℝ N, where u, v = u t, x, v t, x, m and N are positive natural numbers, p, q, r, s > 1, σ, δ ≥ 0, 0 < α, β < 1, and   C D 0, t κ, 0 < κ < 1, is the Caputo fractional derivative of order κ . 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.