摘要
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.
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.
基金
supported by the National Natural Sicence Foundation of China(Nos.11301489,11401367,11501273)
the Natural Science Foundation of Zhejiang Province(Nos.LQ13A010013,LY14A010010)
the Doctoral Fund of Ministry of Education of China(No.20133108120002)
