10.23638/LMCS-13(4:13)2017
https://lmcs.episciences.org/4062
Selivanova, Svetlana
Svetlana
Selivanova
Selivanov, Victor
Victor
Selivanov
Computing Solution Operators of Boundary-value Problems for Some Linear Hyperbolic Systems of PDEs
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
episciences.org
Computer Science - Numerical Analysis
Mathematics - Numerical Analysis
03D78, 58J45, 65M06, 65M25
F.1.1
G.1.8
arXiv.org - Non-exclusive license to distribute
2017-11-21
2017-11-21
2017-11-21
eng
journal article
arXiv:1305.2494
10.48550/arXiv.1305.2494
1860-5974
https://lmcs.episciences.org/4062/pdf
VoR
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Logical Methods in Computer Science
Volume 13, Issue 4
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