On application of the averaging method to the solution of one non-linear integro-differential equation with small parameter of hyperbolic type
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...
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| Date: | 1971 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Russian |
| Published: |
Institute of Mathematics, NAS of Ukraine
1971
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/8511 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |