The authors show the existence and uniqueness of solution for a class of stochastic wave equations with memory. The decay estimate of the energy function of the solution is obtained as well.
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 es...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.展开更多
基金Project supported by the National Natural Science Foundation of China (No. 10871103)
文摘The authors show the existence and uniqueness of solution for a class of stochastic wave equations with memory. The decay estimate of the energy function of the solution is obtained as well.
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)
文摘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.
