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. ContentsIntroductionThe Hele-Shaw problemA joint motion of
two immiscible viscous fluidsMathematical models of in-situ leachingDynamics of cracks in
rocksElements of continuum mechanics
