We propose an algorithm for linearizing systems of partial differential equations at constant solutions. The algorithm is based on an isomorphism constructed between the ring of linearized functions and the ring of special matrices, which makes it possible to simplify calculations in the process of linearization. The algorithm is illustrated by applying it to the quasigasdynamic system.
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D. S. Dummit and R. M. Foote, Abstract Algebra, Wiley, Chichester (2004).
T. G. Elizarova, Quasi-Gas Dynamic Equations, Springer, Berlin, (2009).
A. A. Zlotnik and B. N. Chetverushkin, “Parabolicity of the quasi-gasdynamic system of equations, its hyperbolic second-order modification, an the stability of small perturbations for them,” Comput. Math. Math. Phys. 478, No. 3, 420–446 (2008).
A. A. Zlotnik and T. A. Lomonosov, “L2-dissipativity of the linearized explicit scheme with a kinetic regularization for 2D and 3D gas dynamics system of equations,” Appl. Math. Lett. 103, Article ID 106198 (2020).
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Translated from Problemy Matematicheskogo Analiza 108, 2021, pp. 99-106.
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Lomonosov, T.A. Application of the Homomorphism Theorem for Rings to Linearization of Systems of Partial Differential Equations. J Math Sci 255, 459–466 (2021). https://doi.org/10.1007/s10958-021-05384-5
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DOI: https://doi.org/10.1007/s10958-021-05384-5