The problem of obtaining prescribed distributions of gas parameters

✍ Scribed by S.P. Bautin

• Book ID: 104141981
• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 517 KB
• Volume: 63
• Category: Article
• ISSN: 0021-8928
• DOI: 10.1016/s0021-8928(00)00005-8

✦ Synopsis

Using one-dimensional cylindrically and spherically symmetric flows as examples, the following problem is investigated in which a prescribed density distribution in a gas is obtained: given a known gas flow (background flow), it is required to continuously attach another, unknown gas flow whose density distribution at a fixed instant of time is described by some previously given function.

It is shown that this problem is a characteristic Cauchy problem of standard type for which there is a valid analogue of the Kovalevskaya theorem, provided that the input data are analytic. Other problems of the same type are considered: to ensure that the unknown flow will have a prescribed gas velocity distribution and the prescribed density of the gas in the unknown flow is strictly greater than that of the gas in the background flow (flow with discontinuity). On the assumption that the input data to these problems are analytic, the existence and uniqueness of solutions are proved, in fact--of piecewise analytic solutions. The theorems proved are extended to the case of non-one-dimensional flows.