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
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

Auteur

Anvarbek Meirmanov, Oleg Galtsev, R. Zimin, Yachay Tech, San Miguel de Urcuqui, Equador.

Résumé

"In summary, this is a very interesting book for researchers in the area of mathematical analysis of free boundary problems, especially for those also interested in models related to rock mechanics, like in-situ leaching and propagation of cracks."
Carlos Vázquez Cendón in: Mathematical Reviews Clippings (2018), MR3726920

"The book presents an excellent application of free boundary problems in rock mechanics. [...] The book has a strongly mathematical character in spite of very practical applications from rock and porous mechanics. It can be recommended to graduate students and researchers in engineering and applied mathematics who are interested in deep results on solving free boundary problems and their applications."
Igor Bock in: Zentralblatt MATH 1405.76001