ILL-POSEDNESS IN FLOATING PLATE DYNAMICS

摘要

Motivated by phenomena involving floating ice, a mathematical idealization entailing the dynamic uplift of a floating plate has been looked at by the present authors from two vantage points. In Dempsey et al. (2006), the uplift dynamics are prescribed and it is the forcing that is the unknown. Mathematically, this is an inverse problem which therefore has an inherent level of ill-posedness. In Dempsey & Vasileva (2006), the opposite tack is taken; the uplift forcing is prescribed and the uplift dynamics are determined. Mathematically, the latter is a direct problem. In the first paper, the degree of ill-posedness is ascertained, and in the second it is observed that the "shape" of the uplift dynamics is inherited from the forcing. In a third paper (in this volume), Vasileva & Dempsey (2006), numerical results are computed for two canonical problems using the trapezoidal integration rule. In the present work, the results obtained thus far are summarized so as to put the dynamic uplift problem into perspective as far as the ice mechanics community is concerned.