Nonexistence of global solutions for a time-fractional damped wave equation in a k-times halved space

In this paper, we study the time-fractional damped wave equation (c)D(0)(alpha)u - Delta u + (c)D(0)(beta)u = vertical bar u vertical bar(p), t > 0, x is an element of D-k, where 1 < alpha < 2, 0 < beta < 1, D-c(0)sigma, sigma is an element of {alpha, beta}, is the left-sided Caputo fractional derivative of order sigma with respect to the variable time t,p > 1, and D-k , k is an element of {1, 2, ..., N}, is the k-times halved space given by D-k = {x = (x(1), x(2), ..., x(N)) is an element of R-N : x(i) > 0, i = 1, 2, ..., k}. Using the nonlinear capacity method, we prove that the problem admits no global weak solutions with suitable initial data when 1 < p < 1 + 2 beta/(N+k)beta+2(1-beta) . (C) 2019 Elsevier Ltd. All rights reserved.