Some Bubble and Contact Problems

Solutions of a Class of Mixed Free Boundary Problems

“…When the neck of the channel is much smaller than the distance from the point source to the neck, a matched asymptotic method is employed. Section 4 presents some steady solutions for the membrane problem to illustrate the inequality condition (4). Also the dependence of the steady solution on its history is demonstrated.…”

“…In particular we note that the steady solution, at equals infinity, depends on how the load is brought to the final constant value FF. 4.2. Effect of the history on the location of the load.…”

“…Many physical problems are free or mixed free boundary problems. To name a few from fluid mechanics" jets and wakes [1], interface of bubbles or drops in a fluid [2], [3], [4] and vortices in a stream [5], [6]. Some examples in elasticity and in fracture mechanics are the postbuckling behavior of an elastic tube [7], contact problems involving a buckled elastica [8], peeling of adhesive tape from a surface [9] and splitting of a beam [9].…”

“…The solutions we find exhibit transition or "jump" phenomena. Modifications of the solutions and the changes in the transition phenomena will be presented when the second boundary condition in (2) along the free boundary C1 is replaced by an inequality, i.e., (4) b=0 and 4n=<l, (x,y)eC1.…”

“…When the inequality sign holds on a part of the free boundary C1, then that part will remain stationary during transition, We shall mention two physical problems which are governed respectively by (1), (3) and the equality conditions (2) and by (1), (3) and the inequality condition (4).…”