Interfaces and Mixing Conservation Laws and Boundary Value Problems

This book presents a collection of papers originating from the mini-symposium “Interfaces and Mixing,” held at the International Congress on Industrial and Applied Mathematics (ICIAM) 2023 in Tokyo, Japan. The volume addresses recent advances in the study of interfaces, interfacial mixing, and their nonequilibrium dynamics, which play a central role in a wide range of natural phenomena and technological applications, from supernova explosions and fusion processes to alternative energy technologies and water purification.

The dynamics of interfaces and mixing remain among the most challenging problems in applied mathematics, physics, and engineering. Their mathematical analysis requires the study of conservation laws coupled with singular boundary-value problems and ill-posed initial-value problems, while numerical simulations demand high levels of accuracy, precision, and computational efficiency. These challenges have motivated extensive interdisciplinary research aimed at improving both theoretical understanding and predictive capability.

The papers collected in this volume reflect recent progress in the mathematical modeling, analysis, and numerical simulation of interface dynamics and mixing processes. They highlight new theoretical developments, advanced computational approaches, and emerging applications, while addressing several longstanding questions in the field. By bringing together contributions from leading researchers, this volume provides a timely overview of current directions and achievements in the study of interfaces and mixing.

This book will serve as a valuable reference for researchers, applied mathematicians, engineers, and graduate students interested in the fundamental and applied aspects of interface dynamics, mixing phenomena, and related computational methods.