A class of boundary value problems involving propragation of two-dimensional surface water waves, associated with deep water, against a rigid vertical wall is investigated under the assumption that the surface is covered by a thin sheet of ice. Assuming that the ice-cover behaves like a thin isotropic elastic plate, the problems under consideration lead to those of solving the two-dimensional Laplace equation in a quarter-plane, under a Neumann boundary condition on the vertical boundary and a condition involving upto fifth-order derivatives of the unknown function on the horizontal ice-covered boundary, along with two appropriate edge-conditions, ensuring uniqueness of the solutions. The mixed boundary-value problems are solved completely by determining the unique solution of a special type of integral equation of the first kind.
展开▼
