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 Introduction The HeleShaw problem A joint motion of two immiscible viscous fluids Mathematical models of in-situ leaching Dynamics of cracks in rocks Elements of continuum mechanics
Anvarbek Meirmanov, Oleg Galtsev, R. Zimin, Yachay Tech, San Miguel de Urcuqui, Equador.
