独特性
初值问题
数学
柯西边界条件
柯西问题
双曲型偏微分方程
数学分析
常微分方程
边值问题
分歧(语言学)
订单(交换)
非线性系统
柯西分布
微分方程
椭圆偏微分方程
应用数学
自由边界问题
物理
经济
哲学
量子力学
语言学
财务
出处
期刊:Sbornik Mathematics
[Turpion]
日期:2020-05-01
卷期号:211 (5): 643-688
摘要
Abstract We prove the existence and uniqueness of a solution for the Cauchy problem for a linear abstract second order differential equation, obtain its representation, and prove that it is continuously dependent on the time at which the initial conditions are specified. Based on these results, we prove the existence and uniqueness of a solution of the Cauchy problem for a nonlinear abstract second order differential equation. This result is applied to show that the initial-boundary value problem for a nonlinear hyperbolic divergence structure equation has a unique solution. Bibliography: 49 titles.
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