A numerical study of the wedge - water - entry problem : xed points of separable and mixed - monotonepositive

The wedge-entry problem can be formulated as an integral equation , involving a parameter , small corresponding to wedges of semi-vertex angle just less than =2. An existence proof for the wedge-entry problem is given in LP]. Numerics using a similar integral equation were rst published in Dob], and recently checked and extended to smaller in ZF]. This report contains the following. I Numerical coding and aspects of the existence work are brought closer together. IIa Previously published numerical results are checked (and so far no serious error has been found). IIb The computations are developed as`small-machine' ones, using Matlab, in order to facilitate exploration of subproblems, of different iterations, etc.. IIc The numerical solutions are checked against various bounds given in LP]. III Various items related to unsolved problems concerning thin wedges are collected together. The separable and mixed-monotone operator structure within the problem is exposed. This was motivated by points I, IIb on the list above-and the (long term, not presently realised) hope for a constructive existence proof. This report, related work, and associated numerical (Matlab, etc.) codes are all to be available from links described at