In this monograph, mathematical issues such as existence, uniqueness, regularity, spatially asymptotic and long-time behaviour, and free boundary evolution that concerns a degenerate scalar nonlinear parabolic equation, called the porous medium equation, are systematically addressed. The porous medium equation appears in a number of physical applications, including gas flow through a porous medium, groundwater flow, heat radiation in plasma, problems in population dynamics, diffusion, and lubrication, to name a few. Each chapter contains a detailed introduction and concludes with commentary notes that include historical remarks, recommended further reading and exercises. The book covers the development of the mathematical theory over the last fifty years.

Reviewer:

jomal