Svetlana Selivanova ; Victor Selivanov - Computing Solution Operators of Boundary-value Problems for Some Linear Hyperbolic Systems of PDEs

lmcs:4062 - Logical Methods in Computer Science, November 21, 2017, Volume 13, Issue 4 - https://doi.org/10.23638/LMCS-13(4:13)2017
Computing Solution Operators of Boundary-value Problems for Some Linear Hyperbolic Systems of PDEs

Authors: Svetlana Selivanova ; Victor Selivanov

    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.


    Volume: Volume 13, Issue 4
    Published on: November 21, 2017
    Accepted on: November 21, 2017
    Submitted on: November 14, 2017
    Keywords: Computer Science - Numerical Analysis,Mathematics - Numerical Analysis,03D78, 58J45, 65M06, 65M25,F.1.1,G.1.8

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