Free Boundaries in Rock Mechanics

This monograph is concerned with free-boundary problems of partial differential equations arising in the physical sciences and in engineering. The existence and uniqueness of solutions to the Hele-Shaw problem are derived and techniques to deal with the Muskat problem are discussed. Based on these, mathematical models for the dynamics of cracks in underground rocks and in-situ leaching are developed. 

Contents:

1. Introduction
2. The Hele-Shaw problem
3. A joint motion of two immiscible viscous fluids
4. Mathematical models of in-situ leaching
5. Dynamics of cracks in rocks
6. Elements of continuum mechanics