On application of the averaging method to the solution of one non-linear integro-differential equation with small parameter of hyperbolic type

• Date: 1971
• Main Authors: Melіkіdze, T. V., Меликидзе, Т. В.
• Format: Article
• Language: Russian
• Published: Institute of Mathematics, NAS of Ukraine 1971
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/8511
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

Решение задачи \[u(0,t)=u(l,t)=0,\] \[u|_{t=0}=f_1(x), uʹ_t|_{t=0}=f_2(x)\] для уравнения \[uʹʹ_{tt}-a^2 uʹʹ_{xx}=\gamma u+\varepsilon F(t,x,u,uʹ_t,uʹ_x,\int_0^tf(t,x,u,uʹ_t,uʹ_x){\rm d}y)\] ищется в виде ряда \[u(x,t)=\sum_{n=1}^∞g_n(t,\varepsilon)sin\frac{πn}{l}x\] и для определения $ g_n $ получа...