In this article, by the mean-integral of the conserved quantity, we prove that the one-dimensional non-isentropic gas dynamic equations in an ideal gas state do not possess a bounded invariant region. Moreover, we obtain a necessary condition on the state equations for the existence of an invariant region for a non-isentropic process. Finally, we provide a mathematical example showing that with a special state equation, a bounded invariant region for the non-isentropic process may exist.
Weifeng JIANG
,
Zhen WANG
. THE EXISTENCE OF A BOUNDED INVARIANT REGION FOR COMPRESSIBLE EULER EQUATIONS IN DIFFERENT GAS STATES[J]. Acta mathematica scientia, Series B, 2020
, 40(5)
: 1229
-1239
.
DOI: 10.1007/s10473-020-0505-y
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