This book presents a self-contained introduction to the analytic foundation of a level set method for various surface evolution equations including curvature flow equations. These equations are important for many fields of applications, such as material sciences, image processing and differential geometry. The goal is to introduce a generalized notion of solutions allowing singularities, and to solve the initial-value problem globally-in-time in a generalized sense. Various equivalent definitions of solutions are studied. Several new results on equivalence are also presented. Further, a...
This book presents a self-contained introduction to the analytic foundation of a level set method for various surface evolution equations including cu...
The purpose of this book is to present typical methods (including rescaling methods) for the examination of the behavior of solutions of nonlinear partial di?erential equations of di?usion type. For instance, we examine such eq- tions by analyzing special so-called self-similar solutions. We are in particular interested in equations describing various phenomena such as the Navier- Stokesequations.Therescalingmethod describedherecanalsobeinterpreted as a renormalization group method, which represents a strong tool in the asymptotic analysis of solutions of nonlinear partial di?erential...
The purpose of this book is to present typical methods (including rescaling methods) for the examination of the behavior of solutions of nonlinear par...
This book covers topics ranging from mathematical problems in specific areas to mathematical strategy that helps a leader who must weigh many issues and make timely decisions, to the ways that mathematical literacy helps ensure quality control.
This book covers topics ranging from mathematical problems in specific areas to mathematical strategy that helps a leader who must weigh many issues a...
The aim of this proceeding is addressed to present recent developments of the mathematical research on the Navier-Stokes equations, the Euler equations and other related equations. In particular, we are interested in such problems as: 1) existence, uniqueness and regularity of weak solutions2) stability and its asymptotic behavior of the rest motion and the steady state3) singularity and blow-up of weak and strong solutions4) vorticity and energy conservation5) fluid motions around the rotating axis or outside of the rotating body6) free boundary problems7) maximal regularity theorem...
The aim of this proceeding is addressed to present recent developments of the mathematical research on the Navier-Stokes equations, the Euler equat...
This book covers topics ranging from mathematical problems in specific areas to mathematical strategy that helps a leader who must weigh many issues and make timely decisions, to the ways that mathematical literacy helps ensure quality control.
This book covers topics ranging from mathematical problems in specific areas to mathematical strategy that helps a leader who must weigh many issues a...
This volume consists of eight original survey papers written by invited lecturers in connection with a conference 'Variational Methods for Evolving Objects' held at Hokkaido University, Sapporo, Japan, July 30 - August 3, 2012. The topics of papers vary widely from problems in image processing to dynamics of topological defects, and all involve some nonlinear phenomena of current major research interests. These papers are carefully prepared so that they serve as a good starting point of investigation for graduate students and new comers to the field and are strongly recommended.Published by...
This volume consists of eight original survey papers written by invited lecturers in connection with a conference 'Variational Methods for Evolving Ob...
Mathematics has always played a key role for researches in fluid mechanics. The purpose of this handbook is to give an overview of items that are key to handling problems in fluid mechanics. The first part is devoted to mathematical analysis on incompressible fluids while part 2 is devoted to compressible fluids.
Mathematics has always played a key role for researches in fluid mechanics. The purpose of this handbook is to give an overview of items that are key ...
