We consider the Dirichlet problem for the Laplace equation in a planar domain with a small
hole. The diameter of the hole is proportional to a real parameter ε and we denote by u ε the …

A generalization of the approach developed in the recent papers by the authors is
presented. It aims to provide a description of the Hele-Shaw cell in the presence of multiple …

From Albert Einstein's study (1905) it is known that suspension introduced to a fluid modifies
its viscosity. We propose to describe the influence of obstacles on the Stokesian flow as a …

Asymptotic analysis of the Hele-Shaw flow with a small moving obstacle is performed. The
method of solution utilizes the uniform asymptotic formulas for Green's and Neumann …

Analytical solutions for the one-phase, zero surface tension Hele-Shaw problem describing
the source-driven growth of a blob of viscous fluid in both the exterior and the interior of a …

In the course of this work, the problems which will be examined meet four fundamental
requirements. The first is that the problems are axisymmetric in nature, with a 1D …

A vanishing at infinity solution of the three-dimensional Laplace equation is sought in an a
priori unknown domain with overdetermined boundary conditions, the right-hand sides of …

It is considered the (slow) flow of the viscous incompressible fluid in the Hele-Shaw cell at
presence of a rigid obstacle in the flow. A novel model for such a flow is proposed in terms of …

A vanishing at infinity solution of the three-dimensional Laplace equation is sought in an a
priori unknown domain with overdetermined boundary conditions, the right-hand sides of …

It is considered the (slow) flow of the viscous incompressible fluid in the Hele-Shaw cell at
presence of a rigid obstacle in the flow. A novel model for such a flow is proposed in terms of …