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On conservation laws for hyperbolized equations. (English. Russian original) Zbl 1353.35036

Differ. Equ. 52, No. 7, 817-823 (2016); translation from Differ. Uravn. 52, No. 2, 859-865 (2016).
Summary: We carry out an analysis of hyperbolized equations of diffusion type convenient for modeling on high-performance computer systems; in particular, we study conservation laws for these equations.

MSC:

35B25 Singular perturbations in context of PDEs
35K20 Initial-boundary value problems for second-order parabolic equations
35L20 Initial-boundary value problems for second-order hyperbolic equations
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References:

[1] Chetverushkin, B.N., Kineticheskie skhemy i kvazigazodinamicheskaya sistema uravnenii (Kinematic Schemes and Quasi-Gasdynamic Systems of Equations), Moscow, 2004.
[2] Davydov, A.A., Chetverushkin, B.N., and Shil’nikov, E.V., Modeling the Flows of an Incompressible Fluid and a Weakly Compressible Gas on Multicore Hybrid Computer Systems, Zh. Vychisl. Mat. Mat. Fiz., 2010, vol. 50, no. 12, pp. 2275-2284. · Zbl 1224.65326
[3] Chetverushkin, B.N., D’Aschenzo, N., and Savel’ev, V.I., Kinetically Consistent Equations of Magnetogasdynamics and Their Use in High-Performance Computations, Dokl. Akad. Nauk, 2014, vol. 457, no. 5, pp. 520-529.
[4] Chetverushkin, B.N., D’Aschenzo, N., Ishanov, S., and Saveliev, V., Hyperbolic Type Explicit Kinetic Scheme of Magneto Gas Dynamic for High Performance Computing System, Russian J. Numer. Anal. and Math. Modelling, 2015, vol. 30, no. 1, pp. 27-36. · Zbl 1310.82003 · doi:10.1515/rnam-2015-0003
[5] D’Ascenzo, Savel’ev, V.I., and Chetverushkin, B.N., On an Algorithm for Solving Parabolic and Elliptic Equations, Zh. Vychisl. Mat. Mat. Fiz., 2015, vol. 55, no. 8, pp. 1320-1328.
[6] Chetverushkin, B.N. and Gulin, A.V., Explicit Schemes and Simulation on Ultrahigh Performance Computer Systems, Dokl. Akad. Nauk, 2012, vol. 446, no. 5, pp. 501-503. · Zbl 1393.82001
[7] Repin, S.I. and Chetverushkin, B.N., Estimates for the Difference Between Approximate Solutions of the Cauchy Problem for a Parabolic Diffusion Equation and a Hyperbolic Equation with a Small Parameter, Dokl. Akad. Nauk, 2013, vol. 451, no. 3, pp. 255-258. · Zbl 1277.35033
[8] Myshetskaya, E.E. and Tishkin, V.F., Estimates of the Hyperbolization Effect on the Heat Equation, Zh. Vychisl. Mat. Mat. Fiz., 2015, vol. 55, no. 8, pp. 1299-1304. · Zbl 1328.35068
[9] Myshetskaya, E.E. and Tishkin, V.F., Estimates of the Hyperbolization Effect on the Heat Equation, Preprint IAM, Moscow, 2015, no. 16. · Zbl 1328.35068
[10] Courant, R., Partial Differential Equations (Courant, R. and Hilbert, D., Methods of Mathematical Physics, vol. 2), New York, 1962. Translated under the title Uravneniya s chastnymi proizvodnymi, Moscow: Mir, 1964. · Zbl 0121.07801
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