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Mathematics
At the large significances of gas density it is necessary to take into account [1] balancing radiation and Compton's mechanism of photons dissipative. With methods offered in [2, 3], solutions of nonlinear system of the equations with partial derivatives of the mixed type which describes flows of gas at the specified physical effects are investigated.
The existing of sound characteristic is proved. The velocity of their spreading is strictly less than velocity of sound in the flows of ideal gas. The transport equation describing behavior of derivatives, deducing from the characteristic, is nonlinear and there are flows of considered gas in which on characteristics there is gradient catastrophe. Flows with the thermal heterogeneity extending on not cold gas with final velocity are constructed. As the infinite rows converging in vicinities of considered points (including negative values of time), decisions of a problem about smooth moving the piston in gas and a problem about obtaining preassigned distribution of density, and also analogues centered waves and the partial-compound flows describing strong compression of gas are constructed. Presence of radiant heat conductivity strengthens cumulating effect (it is shown with asymptotic laws of unaccented compression). Are constructed flows which running both on cold, and on not cold background of a wave in heat conductive non-viscous gas. It is shown, that at small velocity of distribution of a wave continuous transition takes place. At increase in the specified velocity there is "an isothermal jump". At the further increase in velocity of movement of a running wave flow again becomes continuous. In situations, transitive from one mode to another, on back front of a running wave the infinite gradient takes place. The analysis of Hugoniot adiabatic curve of considered gas has shown, that at unlimited increase in temperature behind a running wave the attitude of density of gas behind a wave and before a wave without dependence from a polytropic exponent of gas aspires to value 7. Thus it is established, that at $gamma> 4/3$ presence of radiant carry strengthens cumulating effect for density as well at shock influence on gas.
The research is supported by the Russian Foundation for Basic Research, the project 04-01-00205.
1. Zababahin E.I., Zababahin I.E. The phenomena unlimited cumulating. Moscow: Nauka, 1988 (in Russian).
2. Bautin S.P. The mathematical theory of shockless power compression ideal gases. Novosibirsk: Nauka, 1997 (in Russian).
3. Bautin S.P. The analytical heat wave. Moscow: Fizmatlit, 2003 (in Russian).
Note. Abstracts are published in author's edition
Last update: 06-Jul-2012 (11:52:45)