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Decaying positive solutions of some quasilinear differential equations

Tadie — 1998

Commentationes Mathematicae Universitatis Carolinae

The existence of decaying positive solutions in + of the equations ( E λ ) and ( E λ 1 ) displayed below is considered. From the existence of such solutions for the subhomogeneous cases (i.e. t 1 - p F ( r , t U , t | U ' | ) 0 as t ), a super-sub-solutions method (see § 2.2) enables us to obtain existence theorems for more general cases.

Steady vortex rings with swirl in an ideal fluid: asymptotics for some solutions in exterior domains

Tadie — 1999

Applications of Mathematics

In this paper, the axisymmetric flow in an ideal fluid outside the infinite cylinder ( r d ) where ( r , θ , z ) denotes the cylindrical co-ordinates in 3 is considered. The motion is with swirl (i.e. the θ -component of the velocity of the flow is non constant). The (non-dimensional) equation governing the phenomenon is (Pd) displayed below. It is known from e.g. that for the problem without swirl ( f q = 0 in (f)) in the whole space, as the flux constant k tends to , 1) dist ( 0 z , A ) = O ( k 1 / 2 ) ; diam A = O ( exp ( - c 0 k 3 / 2 ) ) ; 2) ( k 1 / 2 Ψ ) k converges to a vortex cylinder U m (see...

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