The focusing problem for the porous medium equation: Experiment, simulation and analysis. (May 2016)

• Record Type: Journal Article
• Authors: Aronson, D.G.
• Is Part Of: Nonlinear analysis. Volume 137(2016)
• Page Start: 135
• Page End: 147
• Publication Date: 2016-05
• Subjects: Focusing porous medium flow -- Convergent gravity flow -- Numerical renormalization; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2015.07.003
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: The focusing problem involves the study of flows which are initially supported outside a compact empty region, with the aim of describing how the flows eventually fill the empty region. The work we describe has its origin in experimental studies of convergent gravity flows and in the global regularity theory of Caffarelli, Vázquez and Wolanski for the equivalent porous medium flow. We give a comprehensive survey of the current state of the experiments, numerical simulations and the analytic studies of this problem. The numerical studies involve innovative renormalization techniques and supply raw material for the analysis.