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On some properties of solutions of transonic potential flow problems

Hans-Peter Gittel (1989)

Aplikace matematiky

The paper deals with solutions of transonic potential flow problems handled in the weak form or as variational inequalities. Using suitable generalized methods, which are well known for elliptic partial differential equations of the second order, some properties of these solutions are derived. A maximum principle, a comparison principle and some conclusions from both ones can be established.

On some properties of the solution of the differential equation u ' ' + 2 u ' r = u - u 3

Valter Šeda, Ján Pekár (1990)

Aplikace matematiky

In the paper it is shown that each solution u ( r , α ) ot the initial value problem (2), (3) has a finite limit for r , and an asymptotic formula for the nontrivial solution u ( r , α ) tending to 0 is given. Further, the existence of such a solutions is established by examining the number of zeros of two different solutions u ( r , α ¯ ) , u ( r , α ^ ) .

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