Giga, Yoshikazu
Overview
Works:  196 works in 336 publications in 2 languages and 2,250 library holdings 

Genres:  Conference papers and proceedings Popular works Miscellanea 
Roles:  Author, Editor 
Classifications:  QA377, 515.353 
Publication Timeline
.
Most widely held works by
Yoshikazu Giga
Surface evolution equations : a level set approach by
Yoshikazu Giga(
Book
)
24 editions published between 2004 and 2006 in English and held by 204 WorldCat member libraries worldwide
This book presents a selfcontained introduction to the analytic foundation of a level set approach for various surface evolution equations including curvature flow equations. These equations are important in many 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 initialvalue problem globallyintime in a generalized sense. Various equivalent definitions of solutions are studied. Several new results on equivalence are also presented. Moreover, structures of level set equations are studied in detail. Further, a rather complete introduction to the theory of viscosity solutions is contained, which is a key tool for the level set approach. Although most of the results in this book are more or less known, they are scattered in several references, sometimes without proofs. This book presents these results in a synthetic way with full proofs. The intended audience are graduate students and researchers in various disciplines who would like to know the applicability and detail of the theory as well as its flavour. No familiarity with differential geometry or the theory of viscosity solutions is required. Only prerequisites are calculus, linear algebra and some basic knowledge about semicontinuous functions
24 editions published between 2004 and 2006 in English and held by 204 WorldCat member libraries worldwide
This book presents a selfcontained introduction to the analytic foundation of a level set approach for various surface evolution equations including curvature flow equations. These equations are important in many 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 initialvalue problem globallyintime in a generalized sense. Various equivalent definitions of solutions are studied. Several new results on equivalence are also presented. Moreover, structures of level set equations are studied in detail. Further, a rather complete introduction to the theory of viscosity solutions is contained, which is a key tool for the level set approach. Although most of the results in this book are more or less known, they are scattered in several references, sometimes without proofs. This book presents these results in a synthetic way with full proofs. The intended audience are graduate students and researchers in various disciplines who would like to know the applicability and detail of the theory as well as its flavour. No familiarity with differential geometry or the theory of viscosity solutions is required. Only prerequisites are calculus, linear algebra and some basic knowledge about semicontinuous functions
Nonlinear partial differential equations : asymptotic behavior of solutions and selfsimilar solutions by
MiHo Giga(
Book
)
21 editions published between 2004 and 2010 in English and held by 147 WorldCat member libraries worldwide
The main focus of this textbook, in two parts, is on showing how selfsimilar solutions are useful in studying the behavior of solutions of nonlinear partial differential equations, especially those of parabolic type. The exposition moves systematically from the basic to more sophisticated concepts with recent developments and several open problems. With challenging exercises, examples, and illustrations to help explain the rigorous analytic basis for the NavierStokes equations, mean curvature flow equations, and other important equations describing real phenomena, this book is written for graduate students and researchers, not only in mathematics but also in other disciplines
21 editions published between 2004 and 2010 in English and held by 147 WorldCat member libraries worldwide
The main focus of this textbook, in two parts, is on showing how selfsimilar solutions are useful in studying the behavior of solutions of nonlinear partial differential equations, especially those of parabolic type. The exposition moves systematically from the basic to more sophisticated concepts with recent developments and several open problems. With challenging exercises, examples, and illustrations to help explain the rigorous analytic basis for the NavierStokes equations, mean curvature flow equations, and other important equations describing real phenomena, this book is written for graduate students and researchers, not only in mathematics but also in other disciplines
What mathematics can do for you : essays and tips from Japanese industry leaders by
Yoshikazu Giga(
Book
)
13 editions published in 2013 in English and held by 34 WorldCat member libraries worldwide
Japan is a tiny country that occupies only 0.25% of the world's total land area. However, this small country is the world's third largest in economy: the Japanese GDP is roughly equivalent to the sum of any two major countries in Europe as of 2012. This book is a first attempt to ask leaders of top Japanese companies, such as Toyota, about their thoughts on mathematics. The topics range from mathematical problems in specific areas (e.g., exploration of natural resources, communication networks, finance) to mathematical strategy that helps a leader who has to weigh many different issues and make
13 editions published in 2013 in English and held by 34 WorldCat member libraries worldwide
Japan is a tiny country that occupies only 0.25% of the world's total land area. However, this small country is the world's third largest in economy: the Japanese GDP is roughly equivalent to the sum of any two major countries in Europe as of 2012. This book is a first attempt to ask leaders of top Japanese companies, such as Toyota, about their thoughts on mathematics. The topics range from mathematical problems in specific areas (e.g., exploration of natural resources, communication networks, finance) to mathematical strategy that helps a leader who has to weigh many different issues and make
Surface evolution equations  a level set method by
Yoshikazu Giga(
Book
)
4 editions published in 2002 in English and held by 9 WorldCat member libraries worldwide
4 editions published in 2002 in English and held by 9 WorldCat member libraries worldwide
Variational methods for evolving objects by Variational methods for evolving objects(
Book
)
4 editions published in 2015 in English and held by 7 WorldCat member libraries worldwide
4 editions published in 2015 in English and held by 7 WorldCat member libraries worldwide
Kyoto Conference on the NavierStokes Equations and their Applications(
Book
)
3 editions published in 2007 in English and held by 7 WorldCat member libraries worldwide
3 editions published in 2007 in English and held by 7 WorldCat member libraries worldwide
Hisenkei henbibun hōteishiki : Kai no zenkin kyodō to jiko sōji kai(
Book
)
2 editions published in 1999 in Japanese and held by 6 WorldCat member libraries worldwide
2 editions published in 1999 in Japanese and held by 6 WorldCat member libraries worldwide
Bibunhōteishikinonenseikairirontosonohatten : kenkyūshūkaihōkokushū(
Book
)
3 editions published between 2005 and 2010 in Japanese and English and held by 6 WorldCat member libraries worldwide
3 editions published between 2005 and 2010 in Japanese and English and held by 6 WorldCat member libraries worldwide
Ugoku kyokumen o oikakete by
Yoshikazu Giga(
Book
)
4 editions published between 1996 and 2015 in Japanese and held by 6 WorldCat member libraries worldwide
4 editions published between 1996 and 2015 in Japanese and held by 6 WorldCat member libraries worldwide
Sūgaku wa yaku ni tatteiruka : Sūgaku ga keizai o ugokasu nihon kigyōhen(
Book
)
2 editions published in 2010 in Japanese and held by 5 WorldCat member libraries worldwide
2 editions published in 2010 in Japanese and held by 5 WorldCat member libraries worldwide
Surface evolution equations A level set approach(
)
1 edition published in 2006 in English and held by 5 WorldCat member libraries worldwide
1 edition published in 2006 in English and held by 5 WorldCat member libraries worldwide
Recent developments of mathematical fluid mechanics(
Book
)
7 editions published in 2016 in English and held by 5 WorldCat member libraries worldwide
The book addresses recent developments of the mathematical research on the NavierStokes and Euler equations as well as on related problems. In particular, there are covered: 1) existence, uniqueness, and the regularity of weak solutions; 2) stability of the motion in rest and the asymptotic behavior of solutions; 3) singularity and blowup of weak and strong solutions; 4) vorticity and energy conservation; 5) motions of rotating fluids, or of fluids surrounding a rotating body; 6) free boundary problems; 7) maximal regularity theory and other abstract results for mathematical fluid mechanics. For this quarter century, these topics have been playing a central role in both pure and applied mathematics and having a great influence to the developm ent of the functional analysis, harmonic analysis and numerical analysis whose tools make a a substantial contribution to the investigation of nonlinear partial differential equations, particularly the NavierStokes and the Euler equations. There are 24 articles in this book in which the nonlinear PDE arising in the fluid mechanics are mainly discussed. The authors consist of speakers and participants of the "International Conference on the Mathematical Fluid Dynamics" on the occasion of Professor Yoshihiro Shibatas 60th birthday held on March 59 in 2013 at old capital city Nara, Japan
7 editions published in 2016 in English and held by 5 WorldCat member libraries worldwide
The book addresses recent developments of the mathematical research on the NavierStokes and Euler equations as well as on related problems. In particular, there are covered: 1) existence, uniqueness, and the regularity of weak solutions; 2) stability of the motion in rest and the asymptotic behavior of solutions; 3) singularity and blowup of weak and strong solutions; 4) vorticity and energy conservation; 5) motions of rotating fluids, or of fluids surrounding a rotating body; 6) free boundary problems; 7) maximal regularity theory and other abstract results for mathematical fluid mechanics. For this quarter century, these topics have been playing a central role in both pure and applied mathematics and having a great influence to the developm ent of the functional analysis, harmonic analysis and numerical analysis whose tools make a a substantial contribution to the investigation of nonlinear partial differential equations, particularly the NavierStokes and the Euler equations. There are 24 articles in this book in which the nonlinear PDE arising in the fluid mechanics are mainly discussed. The authors consist of speakers and participants of the "International Conference on the Mathematical Fluid Dynamics" on the occasion of Professor Yoshihiro Shibatas 60th birthday held on March 59 in 2013 at old capital city Nara, Japan
International Conference for the 25th Anniversary of Viscosity Solutions(
Book
)
3 editions published in 2008 in Japanese and English and held by 4 WorldCat member libraries worldwide
3 editions published in 2008 in Japanese and English and held by 4 WorldCat member libraries worldwide
On blow up rate for signchanging solutions in a convex domain by
Yoshikazu Giga(
Book
)
2 editions published in 2003 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 2003 in English and held by 3 WorldCat member libraries worldwide
Existence of selfsimilar evolution of crystals grown from supersaturated vapor by
Yoshikazu Giga(
Book
)
3 editions published in 2003 in English and held by 3 WorldCat member libraries worldwide
3 editions published in 2003 in English and held by 3 WorldCat member libraries worldwide
Nonlinear waves proceedings of the Fourth MSJ International Research Institute, Sapporo, July 1021, 1995 by
Hokkaidō Daigaku(
Book
)
2 editions published between 1996 and 1997 in English and held by 3 WorldCat member libraries worldwide
2 editions published between 1996 and 1997 in English and held by 3 WorldCat member libraries worldwide
A microscopic time scale approximation to the behavior of the local slope on the faceted surface under a nonuniformity in
supersaturation by
Etsuro Yokoyama(
Book
)
3 editions published in 2007 in English and held by 3 WorldCat member libraries worldwide
3 editions published in 2007 in English and held by 3 WorldCat member libraries worldwide
On the role of kinetic and interfacial anisotropy in the crystal growth theory by
MiHo Giga(
Book
)
3 editions published in 2012 in English and held by 3 WorldCat member libraries worldwide
3 editions published in 2012 in English and held by 3 WorldCat member libraries worldwide
Quasistatic evolution of 3D crystals grown from supersaturated vapor by
Yoshikazu Giga(
Book
)
3 editions published in 2001 in English and held by 3 WorldCat member libraries worldwide
3 editions published in 2001 in English and held by 3 WorldCat member libraries worldwide
Proceedings of the 38th Sapporo Symposium on Partial Differential Equations(
Book
)
3 editions published between 2013 and 2014 in English and held by 3 WorldCat member libraries worldwide
3 editions published between 2013 and 2014 in English and held by 3 WorldCat member libraries worldwide
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Audience Level
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Related Identities
 Giga, MiHo Author
 Saal, Jürgen
 Kobayashi, Toshiyuki 1962 Editor
 Amann, H. (Herbert) 1938 Editor
 Okamoto, Hisashi Editor
 Kozono, Hideo Editor
 Yamazaki, Masao Editor
 Rybka, Piotr
 Ishii, Hitoshi Honoree Author
 Umeda, Noriaki
Associated Subjects
Calculus of variations Continuum (Mathematics) Curves, Algebraic Curves on surfaces Differential equations, Nonlinear Differential equations, Parabolic Differential equations, Partial Evolution equations Fluid mechanicsMathematical models Functional analysis Geometry, Differential Global analysis (Mathematics) Global differential geometry HamiltonJacobi equations Level set methods Mathematical models Mathematical physics Mathematics NavierStokes equations Nonlinear waves Surfaces