一句话：用数值分析与TTE框架证明对称双曲PDE系统边值问题解算子的可计算性。
论文讨论如何将数值分析方法用于在TTE（类型二有效可计算性）框架下证明偏微分方程边值问题解算子的可计算性。作者针对具有可计算实系数和耗散边界条件的对称双曲系统，证明其在立方体 Q 上的边值问题解算子可计算，并证明同一系统的 Cauchy 问题解算子可计算且对系数具有可计算依赖。此类系统可描述弹性、声学、Maxwell方程等广泛物理过程，许多波方程边值问题也可归约到该框架，因此部分回答了 Weihrauch 与 Zhong (2002) 提出的问题。与大多数现有PDE可计算性证明方法相比，该方法不要求存在显式解公式，因而适用于更广一类的方程或方程组。
We discuss possibilities of application of Numerical Analysis methods to proving computability, in the sense of the TTE approach, of solution operators of boundary-value problems for systems of PDEs. We prove computability of the solution operator for a symmetric hyperbolic system with computable real coefficients and dissipative boundary conditions, and of the Cauchy problem for the same system (we also prove computable dependence on the coefficients) in a cube $Q\subseteq\mathbb R^m$. Such systems describe a wide variety of physical processes (e.g. elasticity, acoustics, Maxwell equations). Moreover, many boundary-value problems for the wave equation also can be reduced to this case, thus we partially answer a question raised in Weihrauch and Zhong (2002). Compared with most of other existing methods of proving computability for PDEs, this method does not require existence of explicit solution formulas and is thus applicable to a broader class of (systems of) equations. Comment: 31 pages
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@article{abs-1305-2494,
title = {Computing Solution Operators of Boundary-value Problems for Some Linear Hyperbolic Systems of PDEs},
author = {Svetlana Selivanova and Victor Selivanov},
journal = {Logical Methods in Computer Science},
volume = {Volume 13, Issue 4},
year = {2017},
doi = {10.23638/lmcs-13(4:13)2017}
}