A Generalized Solution of an Initial-Boundary Value Problem Arising in the Mechanics of Discrete-Continuous Systems

E. P. Kubyshkin; O. A. Khrebtyugova

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A Generalized Solution of an Initial-Boundary Value Problem Arising in the Mechanics of Discrete-Continuous Systems

机译：离散连续系统力学中初边值问题的广义解

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摘要

We define a generalized solution of an initial-boundary value problem for a linear system of differential equations with one ordinary differential equation and two partial differential equations (a hybrid system of differential equations). We prove that the problem is well-posed and has a unique generalized solution. An analytical formula for the solution is found. Such systems of differential equations arise in studying discrete-continuum mechanical systems.

机译：我们定义了具有一个常微分方程和两个偏微分方程（一个微分方程的混合系统）的线性微分方程系统的初边值问题的广义解。我们证明问题是适当的，并且具有唯一的广义解决方案。找到该解决方案的解析公式。这样的微分方程系统出现在研究离散连续力学系统中。

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《Automatic Control and Computer Sciences》 |2013年第7期|共10页
作者
E. P. Kubyshkin; O. A. Khrebtyugova;
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原文格式 PDF
正文语种 eng
中图分类自动控制理论;
关键词
Generalized solution; Well posedness of a problem; Discrete-continuum mechanical systems; Timoshenko beam; Analytical solution formula;

机译：广义解;问题的适定性;离散连续力学系统;Timoshenko梁;解析解公式;

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1. A Generalized Solution of an Initial-Boundary Value Problem Arising in the Mechanics of Discrete-Continuous Systems [J] . E. P. Kubyshkin, O. A. Khrebtyugova Automatic Control and Computer Sciences . 2013,第7期

机译：离散连续系统力学中初边值问题的广义解
2. Localized waves and interaction solutions to the fractional generalized CBS-BK equation arising in fluid mechanics [J] . Manafian Jalil, Ilhan Onur Alp, Avazpour Ladan, Advances in Difference Equations . 2021,第a期

机译：流体力学中出现的分数广泛CBS-BK方程的局部波和相互作用解决方案
3. Multiple rogue wave and solitary solutions for the generalized BK equation via Hirota bilinear and SIVP schemes arising in fluid mechanics [J] . Manafian Jalil, Ilhan Onur Alp, Alizadeh Asad, Communications in Theoretical Physics . 2020,第7期

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4. Optimization of Generalized Solutions of Nonlinear Hybrid (Discrete-Continuous) Systems [C] . Boris M. Miller International workshop on hybrid systems: Computation and control . 1998

机译：非线性杂交（离散连续）系统广义解的优化
5. Numerical solutions of matrix equations arising in model reduction of large-scale linear -time -invariant systems. [D] . Nong, Hung Dinh. 2009

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6. Distributed Processing with a Mainframe-Based Hospital Information System: A Generalized Solution [O] . J. David Kirby, Michael P. Pickett, M. William Boyarsky, 1987

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7. Existence, Uniqueness, and Stability of Generalized Solutions of an Initial-Boundary Value Problem for a Degenerating Quasilinear Parabolic Equation [O] . Bürger R, Wendland W.L 1998

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8. Homogeneous and Non-Homogeneous Boundary Value Problems for First Order Linear Hyperbolic Systems Arising in Fluid Mechanics. Part II [R] . da Veiga, H. B. 1982

机译：流体力学中一阶线性双曲型方程的齐次和非齐次边值问题。第二部分

A Generalized Solution of an Initial-Boundary Value Problem Arising in the Mechanics of Discrete-Continuous Systems

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