Blow up for Initial-Boundary Value Problem of Wave Equation with a Nonlinear Memory in 1-D

The present paper is devoted to studying the initial-boundary value problem of a 1-D wave equation with a nonlinear memory： u（tt） - u（xx） = 1/ Γ（1 - γ） ∫0^t （t - s）^（-γ）｜u（s）｜^pds. The blow up result will be established when p 〉 1 and 0 〈 γ 〈 1, no matter how small the initial data are, by introducing two test functions and a new functional.