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Computing solutions of symmetric hyperbolic systems of PDE’s. / Selivanova, Svetlana; Selivanov, Victor.

Proceedings of the 5th International Conference on Computability and Complexity in Analysis, CCA 2008. 2008. p. 243-255.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Harvard

Selivanova, S & Selivanov, V 2008, Computing solutions of symmetric hyperbolic systems of PDE’s. in Proceedings of the 5th International Conference on Computability and Complexity in Analysis, CCA 2008. pp. 243-255. https://doi.org/10.1016/j.entcs.2008.12.021

APA

Selivanova, S., & Selivanov, V. (2008). Computing solutions of symmetric hyperbolic systems of PDE’s. In Proceedings of the 5th International Conference on Computability and Complexity in Analysis, CCA 2008 (pp. 243-255) https://doi.org/10.1016/j.entcs.2008.12.021

Vancouver

Selivanova S, Selivanov V. Computing solutions of symmetric hyperbolic systems of PDE’s. In Proceedings of the 5th International Conference on Computability and Complexity in Analysis, CCA 2008. 2008. p. 243-255 https://doi.org/10.1016/j.entcs.2008.12.021

Author

Selivanova, Svetlana ; Selivanov, Victor. / Computing solutions of symmetric hyperbolic systems of PDE’s. Proceedings of the 5th International Conference on Computability and Complexity in Analysis, CCA 2008. 2008. pp. 243-255

BibTeX

@inproceedings{c98e7e554b7c47288cdde95623573d3f,
title = "Computing solutions of symmetric hyperbolic systems of PDE{\textquoteright}s",
abstract = "We study the computability properties of symmetric hyperbolic systems of PDE{\textquoteright}s (Formula presented.), with the initial condition u|t=0 = φ(x1, . . ., xm). Such systems first considered by K.O. Friedrichs can be used to describe a wide variety of physical processes. Using the difference equations approach, we prove computability of the operator that sends (for any fixed computable matrices A, B1, . . ., Bm satisfying some natural conditions) any initial function φ ∈ Ck+1(Q, ℝn), k ≥ 1, to the unique solution u ∈ Ck(H, ℝn), where Q = [0, 1]m and H is the nonempty domain of correctness of the system.",
keywords = "Computability, Difference scheme, Finite-dimensional approximation, Hyperbolic system, Matrix pencil, Metric space, Norm, PDE, Stability",
author = "Svetlana Selivanova and Victor Selivanov",
year = "2008",
month = jan,
day = "1",
doi = "10.1016/j.entcs.2008.12.021",
language = "English",
pages = "243--255",
booktitle = "Proceedings of the 5th International Conference on Computability and Complexity in Analysis, CCA 2008",

}

RIS

TY - GEN

T1 - Computing solutions of symmetric hyperbolic systems of PDE’s

AU - Selivanova, Svetlana

AU - Selivanov, Victor

PY - 2008/1/1

Y1 - 2008/1/1

N2 - We study the computability properties of symmetric hyperbolic systems of PDE’s (Formula presented.), with the initial condition u|t=0 = φ(x1, . . ., xm). Such systems first considered by K.O. Friedrichs can be used to describe a wide variety of physical processes. Using the difference equations approach, we prove computability of the operator that sends (for any fixed computable matrices A, B1, . . ., Bm satisfying some natural conditions) any initial function φ ∈ Ck+1(Q, ℝn), k ≥ 1, to the unique solution u ∈ Ck(H, ℝn), where Q = [0, 1]m and H is the nonempty domain of correctness of the system.

AB - We study the computability properties of symmetric hyperbolic systems of PDE’s (Formula presented.), with the initial condition u|t=0 = φ(x1, . . ., xm). Such systems first considered by K.O. Friedrichs can be used to describe a wide variety of physical processes. Using the difference equations approach, we prove computability of the operator that sends (for any fixed computable matrices A, B1, . . ., Bm satisfying some natural conditions) any initial function φ ∈ Ck+1(Q, ℝn), k ≥ 1, to the unique solution u ∈ Ck(H, ℝn), where Q = [0, 1]m and H is the nonempty domain of correctness of the system.

KW - Computability

KW - Difference scheme

KW - Finite-dimensional approximation

KW - Hyperbolic system

KW - Matrix pencil

KW - Metric space

KW - Norm

KW - PDE

KW - Stability

UR - http://www.scopus.com/inward/record.url?scp=85067181850&partnerID=8YFLogxK

U2 - 10.1016/j.entcs.2008.12.021

DO - 10.1016/j.entcs.2008.12.021

M3 - Conference contribution

AN - SCOPUS:85067181850

SP - 243

EP - 255

BT - Proceedings of the 5th International Conference on Computability and Complexity in Analysis, CCA 2008

ER -

ID: 127087536