Far Eastern Mathematical Journal

To content of the issue


Analysis of the uniqueness and stability of hyperbolic-parabolic system


Amosova E.V.

2016, issue 2, Ñ. 123-136


Abstract
À theorem of existence and uniqueness for hyperbolic-parabolic system of equations conjugate to compressible Navier-Stokes equations is proved.

Keywords:
transport equation, hyperbolic-parabolic system

Download the article (PDF-file)

References

[1] A.V. Fursikov, O.Yu. Imanuvilov, “On controllability of certain systems simulating a fluid flow”, IMA Vol. Math. Appl., 68 (1995), 149–184.
[2] A. V. Fursikov, O.Yu. Imanuvilov, “On exact boundary zero-controllability of two-dimensional Navier-Stokes equations”, Acta Appl. Math., 37 (1994), 67–76.
[3] A. V. Fursikov, Optimal'noe upravlenie raspredelitel'nymi sistemami. Teoriia i prilozheniia, Nauchnaia kniga, N., 1999.
[4] G. Fichera, “Sulle equazioni differenziali lineari elliptico-paraboliche del secondo ordine”, Atti Accad. naz. Lincey, Mem. Cl. sci. fis., mat. e natur., 5(1) (1956), P.30.
[5] O. A. Oleinik, E. V. Radkevich, Second order equation with non-negative characteristic form, New York-London, American Math. Soc., Providence, Rhode Island Plenum Press, 1973.
[6] R.J. Di Perna, P.L. Lions, “Ordinary differential equations, transport theory and Sobolev spaces”, Invent. Math., 98 (1989), 511–547.
[7] L. Ambrosio, “Transport equation and Cauchy problem for BV vector fields”, Invent. Math., 158(2) (2004), 227–260.
[8] P. Plotnikov, J. Sokolowski, Compressible Navier-Stokes equations. Theory and shape optimization, Birkhauser, 2012.
[9] B.L. Rozhdestvenskii, N.N. Ianenko, Sistemy kvazilineinykh uravnenii i ikh prilozheniia k gazovoi dinamike, Nauka, M., 1968.
[10] O.A. Ladyzhenskaia, Kraevye zadachi matematicheskoi fiziki, Nauka, M., 1973.
[11] Zh.L. Lions, E. Madzhenes, Neodnorodnye granichnye zadachi i ikh prilozheniia, Mir, M., 1971.

To content of the issue