The Porous Medium Equation - Mathematical Theory
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.