Nonexistence of global solutions for a time-fractional damped wave equation in a [formula omitted]-times halved space

Abstract

In this paper, we study the time-fractional damped wave equation CD0αu−Δu+CD0βu=|u|p,t>0,x∈Dk,where 1<α<2, 0<β<1, CD0σ, σ∈{α,β}, is the left-sided Caputo fractional derivative of order σ with respect to the variable time t, p>1, and Dk, k∈{1,2,…,N}, is the k-times halved space given by Dk={x=(x1,x2,…,xN)∈RN:xi>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+2β(N+k)β+2(1−β).