Yoshikazu Giga – författare
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16 produkter
16 produkter
Inbunden, Engelska, 2010
972 kr
Skickas inom 10-15 vardagar
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 equations. Although such asymptotic analysis is used formally in various disciplines, not seldom there is a lack of a rigorous mathematical treatment. The intention of this monograph is to ?ll this gap. We intend to develop a rigorous mat- matical foundation of such a formalasymptotic analysis related to self-similar solutions. A self-similar solution is, roughly speaking, a solution invariant under a scaling transformationthat does not change the equation. For several typical equations we shall give mathematical proofs that certain self-similar solutions asymptotically approximate the typical behavior of a wide class of solutions. Since nonlinear partial di?erential equations are used not only in mat- matics but also in various ?elds of science and technology, there is a huge variety of approaches. Moreover,even the attempt to cover only a few typical ?elds and methods requires many pages of explanations and collateral tools so that the approaches are self-contained and accessible to a large audience.
E-bok
PDF, Engelska, 20101 258 kr
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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 equations. Although such asymptotic analysis is used formally in various disciplines, not seldom there is a lack of a rigorous mathematical treatment. The intention of this monograph is to ?ll this gap. We intend to develop a rigorous mat- matical foundation of such a formalasymptotic analysis related to self-similar solutions. A self-similar solution is, roughly speaking, a solution invariant under a scaling transformationthat does not change the equation. For several typical equations we shall give mathematical proofs that certain self-similar solutions asymptotically approximate the typical behavior of a wide class of solutions. Since nonlinear partial di?erential equations are used not only in mat- matics but also in various ?elds of science and technology, there is a huge variety of approaches. Moreover,even the attempt to cover only a few typical ?elds and methods requires many pages of explanations and collateral tools so that the approaches are self-contained and accessible to a large audience.
Häftad, Engelska, 2023
650 kr
Skickas inom 10-15 vardagar
This book addresses the issue of uniqueness of a solution to a problem – a very important topic in science and technology, particularly in the field of partial differential equations, where uniqueness guarantees that certain partial differential equations are sufficient to model a given phenomenon. This book is intended to be a short introduction to uniqueness questions for initial value problems. One often weakens the notion of a solution to include non-differentiable solutions. Such a solution is called a weak solution. It is easier to find a weak solution, but it is more difficult to establish its uniqueness. This book examines three very fundamental equations: ordinary differential equations, scalar conservation laws, and Hamilton-Jacobi equations. Starting from the standard Gronwall inequality, this book discusses less regular ordinary differential equations. It includes an introduction of advanced topics like the theory of maximal monotone operators as wellas what is called DiPerna-Lions theory, which is still an active research area. For conservation laws, the uniqueness of entropy solution, a special (discontinuous) weak solution is explained. For Hamilton-Jacobi equations, several uniqueness results are established for a viscosity solution, a kind of a non-differentiable weak solution. The uniqueness of discontinuous viscosity solution is also discussed. A detailed proof is given for each uniqueness statement. The reader is expected to learn various fundamental ideas and techniques in mathematical analysis for partial differential equations by establishing uniqueness. No prerequisite other than simple calculus and linear algebra is necessary. For the reader’s convenience, a list of basic terminology is given at the end of this book.
E-bok
Engelska, 2023870 kr
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This book addresses the issue of uniqueness of a solution to a problem – a very important topic in science and technology, particularly in the field of partial differential equations, where uniqueness guarantees that certain partial differential equations are sufficient to model a given phenomenon.
This book is intended to be a short introduction to uniqueness questions for initial value problems. One often weakens the notion of a solution to include non-differentiable solutions. Such a solution is called a weak solution. It is easier to find a weak solution, but it is more difficult to establish its uniqueness. This book examines three very fundamental equations: ordinary differential equations, scalar conservation laws, and Hamilton-Jacobi equations. Starting from the standard Gronwall inequality, this book discusses less regular ordinary differential equations. It includes an introduction of advanced topics like the theory of maximal monotone operators as wellas what is called DiPerna-Lions theory, which is still an active research area. For conservation laws, the uniqueness of entropy solution, a special (discontinuous) weak solution is explained. For Hamilton-Jacobi equations, several uniqueness results are established for a viscosity solution, a kind of a non-differentiable weak solution. The uniqueness of discontinuous viscosity solution is also discussed. A detailed proof is given for each uniqueness statement.
The reader is expected to learn various fundamental ideas and techniques in mathematical analysis for partial differential equations by establishing uniqueness. No prerequisite other than simple calculus and linear algebra is necessary. For the reader’s convenience, a list of basic terminology is given at the end of this book.
- Nyhet
Inbunden, Engelska, 2026
2 503 kr
Skickas inom 3-6 vardagar
This monograph presents a self-contained 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 initial-value problem globally-in-time in a generalized sense. For the Second Edition, new chapters have been added that describe a recent approach to surface evolution equations based on deterministic discrete two-person games. This game-theoretic interpretation is used to discuss the fattening phenomenon for the curvature flow equation and to provide an alternative proof for convexity preserving properties.This text is suitable for applied researchers who would like to know the detail of the theory, as well as its flavor; it is also suitable for graduate students interested in the field. Prerequisites include calculus, linear algebra, and some familiarity with semicontinuous functions. Familiarity with differential geometry and the theory of viscosity solutions is not required.
Inbunden, Engelska, 2016
1 079 kr
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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 and other abstract theorems for mathematical fluid mechanics.
E-bok
PDF, Engelska, 20161 416 kr
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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 and other abstract theorems for mathematical fluid mechanics.
31 626 kr
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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. Since the field of fluid mechanics is huge, it is almost impossible to cover many topics. In this handbook, we focus on mathematical analysis on viscous Newtonian fluid. The first part is devoted to mathematical analysis on incompressible fluids while part 2 is devoted to compressible fluids.
E-bok
Engelska, 201831 641 kr
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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. Since the field of fluid mechanics is huge, it is almost impossible to cover many topics. In this handbook, we focus on mathematical analysis on viscous Newtonian fluid. The first part is devoted to mathematical analysis on incompressible fluids while part 2 is devoted to compressible fluids.
Inbunden, Engelska, 2006
1 723 kr
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This book is intended to be a self-contained introduction to analytic foundations of a level set method for various surface evolution equations including curvature ?ow equations. These equations are important in various ?elds including material sciences, image processing and di?erential geometry. The goal of this book is to introduce a generalized notion of solutions allowing singularities and solve the initial-value problem globally-in-time in a generalized sense. Various equivalent de?nitions of solutions are studied. Several new results on equivalence are also presented. Wepresentherearathercompleteintroductiontothetheoryofviscosityso- tionswhichis a keytoolforthe levelsetmethod. Alsoa self-containedexplanation isgivenforgeneralsurfaceevolutionequationsofthe secondorder.Althoughmost ofthe resultsin this book aremoreor lessknown,they arescatteredinseveralr- erences, sometimes without proof. This book presents these results in a synthetic way with full proofs. However, the references are not exhaustive at all. The book is suitable for applied researchers who would like to know the detail of the theory as well as its ?avour.No familiarity with di?erential geometry and the theory of viscosity solutions is required.The prerequisites are calculus, linear algebra and some familiarity with semicontinuous functions. This book is also suitable for upper level under graduate students who are interested in the ?eld.
Inbunden, Engelska, 2006
2 207 kr
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Inbunden, Engelska, 2013
543 kr
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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 decisions in a timely manner, and even to mathematical literacy that ensures quality control. The reader may notice that every article reflects the authors’ way of life and thinking, which can be evident in even one sentence.This book is an enlarged English edition of the Japanese book What Mathematics Can Do for You: Essays and Tips from Japanese Industry Leaders. In this edition we have invited the contributions of three mathematicians who have been working to expand and strengthen the interaction between mathematics and industry.The role of mathematics is usually invisible when it is applied effectively and smoothly in science and technology, and mathematical strategy is often hidden when it is used properly and successfully. The business leaders in successful top Japanese companies are well aware of this invisible feature of mathematics in applications aside from the intrinsic depth of mathematics. What Mathematics Can Do forYou ultimately provides the reader an opportunity to notice what is hidden but key to business strategy.
E-bok
PDF, Engelska, 2013712 kr
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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 decisions in a timely manner, and even to mathematical literacy that ensures quality control. The reader may notice that every article reflects the authors’ way of life and thinking, which can be evident in even one sentence.This book is an enlarged English edition of the Japanese book What Mathematics Can Do for You: Essays and Tips from Japanese Industry Leaders. In this edition we have invited the contributions of three mathematicians who have been working to expand and strengthen the interaction between mathematics and industry.The role of mathematics is usually invisible when it is applied effectively and smoothly in science and technology, and mathematical strategy is often hidden when it is used properly and successfully. The business leaders in successful top Japanese companies are well aware of this invisible feature of mathematics in applications aside from the intrinsic depth of mathematics. What Mathematics Can Do forYou ultimately provides the reader an opportunity to notice what is hidden but key to business strategy.
Häftad, Engelska, 2015
543 kr
Skickas inom 10-15 vardagar
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 decisions in a timely manner, and even to mathematical literacy that ensures quality control. The reader may notice that every article reflects the authors’ way of life and thinking, which can be evident in even one sentence.This book is an enlarged English edition of the Japanese book What Mathematics Can Do for You: Essays and Tips from Japanese Industry Leaders. In this edition we have invited the contributions of three mathematicians who have been working to expand and strengthen the interaction between mathematics and industry.The role of mathematics is usually invisible when it is applied effectively and smoothly in science and technology, and mathematical strategy is often hidden when it is used properly and successfully. The business leaders in successful top Japanese companies are well aware of this invisible feature of mathematics in applications aside from the intrinsic depth of mathematics. What Mathematics Can Do forYou ultimately provides the reader an opportunity to notice what is hidden but key to business strategy.
Del 85 - Advanced Studies in Pure Mathematics
Role Of Metrics In The Theory Of Partial Differential, The - Proceedings Of The 11th Mathematical Society Of Japan, Seasonal Institute (Msj-si)
Inbunden, Engelska, 2021
1 247 kr
Skickas inom 5-8 vardagar
This volume is edited as the proceedings of the 11th Mathematical Society of Japan, Seasonal Institute (MSJ-SI) "The Role of Metrics in the Theory of Partial Differential Equations", held for the period of July 2-13, 2018 in Hokkaido University, Sapporo, Japan. This volume consists of peer-reviewed articles written by speakers who actively lead the fields of partial differential equations, numerical analysis, harmonic analysis, and geometric analysis. It should be underlined that 3 survey articles provided by course lecturers show an interesting direction of analysis under various metrics. This volume is suitable for any graduate students and young researchers to motivate the research on these fields from the viewpoint of metrics.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets except North America
Inbunden, Engelska, 2015
913 kr
Tillfälligt slut
This volume consists of eight original survey papers written by invited lecturers in connection with a conference “Variational Methods for Evolving Objects”. 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.