TY - JOUR

T1 - Computing solution operators of boundary-value problems for some linear hyperbolic systems of pdes

AU - Selivanova, Svetlana

AU - Selivanov, Victor

PY - 2017

Y1 - 2017

N2 - We discuss possibilities of application of Numerical Analysis methods to proving computability, in the sense of the TTE approach, of solution operators of boundaryvalue 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 ⊆ ℝm. Such systems describe a wide variety of physical processes (e.g. elasticity, acoustics, Maxwell equations). Moreover, many boundaryvalue problems for the wave equation also can be reduced to this case, thus we partially answer a question raised in [WZ02]. 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.

AB - We discuss possibilities of application of Numerical Analysis methods to proving computability, in the sense of the TTE approach, of solution operators of boundaryvalue 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 ⊆ ℝm. Such systems describe a wide variety of physical processes (e.g. elasticity, acoustics, Maxwell equations). Moreover, many boundaryvalue problems for the wave equation also can be reduced to this case, thus we partially answer a question raised in [WZ02]. 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.

KW - Algebraic real

KW - Boundary-value problem

KW - Cauchy problem

KW - Computability

KW - Constructive field

KW - Difference scheme

KW - Finite-dimensional approximation

KW - Solution operator

KW - Stability

KW - Symmetric hyperbolic system

KW - Systems of PDEs

KW - Wave equation

UR - http://www.scopus.com/inward/record.url?scp=85041855765&partnerID=8YFLogxK

U2 - 10.23638/LMCS-13(4:13)2017

DO - 10.23638/LMCS-13(4:13)2017

M3 - Article

AN - SCOPUS:85041855765

VL - 13

JO - Logical Methods in Computer Science

JF - Logical Methods in Computer Science

SN - 1860-5974

IS - 4

M1 - 13

ER -