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Preface
Construction and research of adequate computational models for quasilinear hyperbolic systems
1. | National University of Uzbekistan, Faculty of Mathematics, 4, Universitetskaya str., Tashkent, Uzbekistan |
2. | Sobolev Institute of Mathematics, 4, Acad. Koptyug str., Novosibirsk, Russia |
In the paper, we study a class of three-dimensional quasilinear hyperbolic systems. For such system, we set the initial boundary value problem and construct the energy integral. We construct the difference scheme and obtain an a priori estimate for its solution.
References:
[1] |
R. D. Aloev, Z. K. Eshkuvatov, Sh. O. Davlatov and N. M. A. Nik Long,
Sufficient condition of stability of finite element method for symmetric t-hyperbolic systems with constant coefficients, Computers and Mathematics with Applications, 68 (2014), 1194-1204.
doi: 10.1016/j.camwa.2014.08.019. |
[2] |
R. D. Aloev, A. M. Blokhin and M. U. Hudayberganov,
One class of stable difference schemes for hyperbolic system, American Journal of Numerical Analysis, 2 (2014), 85-89.
|
[3] |
A. M. Blokhin and R. D. Aloev, Energy Integrals and Their Applications to Investigation of Stability of Difference Schemes, Novosibirsk, 1993. 224 p(in Russian). |
[4] |
S. K. Godunov, Equations of Mathematical Physics, Nauka, Moscow, 1979 (in Russian). |
[5] |
S. K. Godunov, An interesting class of quasi-linear systems, Dokl. Akad. Nauk SSSR, 139 (1961), 521–523. (in Russian). |
[6] |
S. K. Godunov and E. I. Romenskii, Elements of Continuum Mechanics and Conservation Laws, Springer-Verlag, New York, 2003.
doi: 10.1007/978-1-4757-5117-8. |
[7] |
A. Harten,
On the symmetric form of systems of conservation laws with entropy, J. Comp. Phys., 49 (1983), 151-164.
doi: 10.1016/0021-9991(83)90118-3. |
[8] |
A. I. Vol'pert and S. I. Khudyaev,
On the Cauchy problem for composite systems of nonlinear differential equations, Math. USSR Sb., 16 (1972), 517-544.
doi: 10.1070/SM1972v016n04ABEH001438. |
[9] |
Yu. S. Zavyalov, B. I. Kvasov and V. L. Miroshnichenko, Methods of Spline Functions, Moscow, Nauka, 1980 (in Russian). |
show all references
References:
[1] |
R. D. Aloev, Z. K. Eshkuvatov, Sh. O. Davlatov and N. M. A. Nik Long,
Sufficient condition of stability of finite element method for symmetric t-hyperbolic systems with constant coefficients, Computers and Mathematics with Applications, 68 (2014), 1194-1204.
doi: 10.1016/j.camwa.2014.08.019. |
[2] |
R. D. Aloev, A. M. Blokhin and M. U. Hudayberganov,
One class of stable difference schemes for hyperbolic system, American Journal of Numerical Analysis, 2 (2014), 85-89.
|
[3] |
A. M. Blokhin and R. D. Aloev, Energy Integrals and Their Applications to Investigation of Stability of Difference Schemes, Novosibirsk, 1993. 224 p(in Russian). |
[4] |
S. K. Godunov, Equations of Mathematical Physics, Nauka, Moscow, 1979 (in Russian). |
[5] |
S. K. Godunov, An interesting class of quasi-linear systems, Dokl. Akad. Nauk SSSR, 139 (1961), 521–523. (in Russian). |
[6] |
S. K. Godunov and E. I. Romenskii, Elements of Continuum Mechanics and Conservation Laws, Springer-Verlag, New York, 2003.
doi: 10.1007/978-1-4757-5117-8. |
[7] |
A. Harten,
On the symmetric form of systems of conservation laws with entropy, J. Comp. Phys., 49 (1983), 151-164.
doi: 10.1016/0021-9991(83)90118-3. |
[8] |
A. I. Vol'pert and S. I. Khudyaev,
On the Cauchy problem for composite systems of nonlinear differential equations, Math. USSR Sb., 16 (1972), 517-544.
doi: 10.1070/SM1972v016n04ABEH001438. |
[9] |
Yu. S. Zavyalov, B. I. Kvasov and V. L. Miroshnichenko, Methods of Spline Functions, Moscow, Nauka, 1980 (in Russian). |


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