Abstract:
The basic ideas and results of investigations of the effect on a compressible medium of a special class of gas-dynamic and thermal regimes (regimes with peaking) are expounded. A mathematical description is given of new phenomena caused by such effects (the effect of localization, formation of structures, shockless compression of continuous media). The mathematical model studied was used in a number of applications, in particular, to problems of the physics of plasmas.
Citation:
N. V. Zmitrenko, S. P. Kurdyumov, A. P. Mikhailov, “The theory of modes with peaking in compressible media”, Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Nov. Dostizh., 28, VINITI, Moscow, 1986, 3–94; J. Soviet Math., 41:5 (1988), 1163–1222
\Bibitem{ZmiKurMik86}
\by N.~V.~Zmitrenko, S.~P.~Kurdyumov, A.~P.~Mikhailov
\paper The theory of modes with peaking in compressible media
\serial Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Nov. Dostizh.
\yr 1986
\vol 28
\pages 3--94
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/intd91}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=894258}
\zmath{https://zbmath.org/?q=an:0850.76566|0689.76021}
\transl
\jour J. Soviet Math.
\yr 1988
\vol 41
\issue 5
\pages 1163--1222
\crossref{https://doi.org/10.1007/BF01098784}
Linking options:
https://www.mathnet.ru/eng/intd91
https://www.mathnet.ru/eng/intd/v28/p3
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Milena Dimova, Stefka Dimova, Lecture Notes in Computer Science, 6046, Numerical Methods and Applications, 2011, 395
G. V. Dolgoleva, A. V. Zabrodin, “Computational construction of microtargets for shockless compression”, Proc. Steklov Inst. Math. (Suppl.), 261, suppl. 1 (2008), S44–S54
G. V. Dolgoleva, A. V. Zabrodin, O. B. Khairullina, “Computational construction of the microtargets on the basis of realization of shockless compression conception”, Proc. Steklov Inst. Math. (Suppl.), 2003no. , suppl. 2, S8–S23
V. A. Belavin, S. P. Kurdyumov, “Blow-up regimes in a demographic system: Scenario of increase in the nonlinearity”, Comput. Math. Math. Phys., 40:2 (2000), 227–239
V. Yu. Bychenkov, V. P. Silin, V. T. Tihonchyuk, “Two-dimensional vortex structures in an anisotropic plasma”, Theoret. and Math. Phys., 82:1 (1990), 11–18
V. V. Gudkov, A. P. Mikhailov, V. V. Stepanova, “Localized compression regimes in a heat-conducting gas”, U.S.S.R. Comput. Math. Math. Phys., 30:2 (1990), 130–138
V. A. Galaktionov, S. P. Kurdyumov, A. A. Samarskii, “On the method of stationary states for quasilinear parabolic equations”, Math. USSR-Sb., 67:2 (1990), 449–471
O. G. Kharlampovich, “The word problem for solvable Lie algebras and groups”, Math. USSR-Sb., 67:2 (1990), 489–525
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