Author: John Michael Rassias
Publisher: World Scientific
ISBN: 9789810204068
Category : Mathematics
Languages : en
Pages : 160
Book Description
This book discusses various parts of the theory of mixed type partial differential equations with boundary conditions such as: Chaplygin's classical dynamical equation of mixed type, the theory of regularity of solutions in the sense of Tricomi, Tricomi's fundamental idea and one-dimensional singular integral equations on non-Carleman type, Gellerstedt's characteristic problem and Frankl's non-characteristic problem, Bitsadze and Lavrentjev's mixed type boundary value problems, quasi-regularity of solutions in the classical sense. Some of the latest results of the author are also presented in this book.
Lecture Notes on Mixed Type Partial Differential Equations
Author: John Michael Rassias
Publisher: World Scientific
ISBN: 9789810204068
Category : Mathematics
Languages : en
Pages : 160
Book Description
This book discusses various parts of the theory of mixed type partial differential equations with boundary conditions such as: Chaplygin's classical dynamical equation of mixed type, the theory of regularity of solutions in the sense of Tricomi, Tricomi's fundamental idea and one-dimensional singular integral equations on non-Carleman type, Gellerstedt's characteristic problem and Frankl's non-characteristic problem, Bitsadze and Lavrentjev's mixed type boundary value problems, quasi-regularity of solutions in the classical sense. Some of the latest results of the author are also presented in this book.
Publisher: World Scientific
ISBN: 9789810204068
Category : Mathematics
Languages : en
Pages : 160
Book Description
This book discusses various parts of the theory of mixed type partial differential equations with boundary conditions such as: Chaplygin's classical dynamical equation of mixed type, the theory of regularity of solutions in the sense of Tricomi, Tricomi's fundamental idea and one-dimensional singular integral equations on non-Carleman type, Gellerstedt's characteristic problem and Frankl's non-characteristic problem, Bitsadze and Lavrentjev's mixed type boundary value problems, quasi-regularity of solutions in the classical sense. Some of the latest results of the author are also presented in this book.
Mixed Type Partial Differential Equations, Lecture Notes On
Author: Rassias John Michael
Publisher: World Scientific Publishing Company
ISBN: 9813103647
Category : Mathematics
Languages : en
Pages : 152
Book Description
This book discusses various parts of the theory of mixed type partial differential equations with boundary conditions such as: Chaplygin's classical dynamical equation of mixed type, the theory of regularity of solutions in the sense of Tricomi, Tricomi's fundamental idea and one-dimensional singular integral equations on non-Carleman type, Gellerstedt's characteristic problem and Frankl's non-characteristic problem, Bitsadze and Lavrentjev's mixed type boundary value problems, quasi-regularity of solutions in the classical sense. Some of the latest results of the author are also presented in this book.
Publisher: World Scientific Publishing Company
ISBN: 9813103647
Category : Mathematics
Languages : en
Pages : 152
Book Description
This book discusses various parts of the theory of mixed type partial differential equations with boundary conditions such as: Chaplygin's classical dynamical equation of mixed type, the theory of regularity of solutions in the sense of Tricomi, Tricomi's fundamental idea and one-dimensional singular integral equations on non-Carleman type, Gellerstedt's characteristic problem and Frankl's non-characteristic problem, Bitsadze and Lavrentjev's mixed type boundary value problems, quasi-regularity of solutions in the classical sense. Some of the latest results of the author are also presented in this book.
Mixed Problem for Partial Differential Equations with Quasihomogeneous Principal Part
Author: Semen Grigorʹevich Gindikin
Publisher: American Mathematical Soc.
ISBN: 9780821846179
Category : Mathematics
Languages : en
Pages : 233
Book Description
This book offers the first systematic presentation of the theory of the mixed problem for hyperbolic differential equations with variable coefficients. This class includes hyperbolic and parabolic equations as well as nonclassic type of operator - the $q$-hyperbolic equation - which was introduced by the authors. As part of the exposition, the authors consider the Cauchy problem for this class of equations. This book would be suitable as a graduate textbook for courses in partial differential equations.
Publisher: American Mathematical Soc.
ISBN: 9780821846179
Category : Mathematics
Languages : en
Pages : 233
Book Description
This book offers the first systematic presentation of the theory of the mixed problem for hyperbolic differential equations with variable coefficients. This class includes hyperbolic and parabolic equations as well as nonclassic type of operator - the $q$-hyperbolic equation - which was introduced by the authors. As part of the exposition, the authors consider the Cauchy problem for this class of equations. This book would be suitable as a graduate textbook for courses in partial differential equations.
Partial Differential Equations
Author: Walter A. Strauss
Publisher: John Wiley & Sons
ISBN: 0470054565
Category : Mathematics
Languages : en
Pages : 467
Book Description
Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.
Publisher: John Wiley & Sons
ISBN: 0470054565
Category : Mathematics
Languages : en
Pages : 467
Book Description
Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.
Introduction to Partial Differential Equations of Mixed Type
Author: Michael Schneider
Publisher:
ISBN:
Category : Differential equations, Partial
Languages : en
Pages : 126
Book Description
Publisher:
ISBN:
Category : Differential equations, Partial
Languages : en
Pages : 126
Book Description
Lectures on Mixed Problems in Partial Differential Equations and Representation of Semi-groups
Author: Laurent Schwartz
Publisher:
ISBN:
Category : Differential equations, Partial
Languages : en
Pages : 270
Book Description
Publisher:
ISBN:
Category : Differential equations, Partial
Languages : en
Pages : 270
Book Description
Elliptic–Hyperbolic Partial Differential Equations
Author: Thomas H. Otway
Publisher: Springer
ISBN: 3319197614
Category : Mathematics
Languages : en
Pages : 134
Book Description
This text is a concise introduction to the partial differential equations which change from elliptic to hyperbolic type across a smooth hypersurface of their domain. These are becoming increasingly important in diverse sub-fields of both applied mathematics and engineering, for example: • The heating of fusion plasmas by electromagnetic waves • The behaviour of light near a caustic • Extremal surfaces in the space of special relativity • The formation of rapids; transonic and multiphase fluid flow • The dynamics of certain models for elastic structures • The shape of industrial surfaces such as windshields and airfoils • Pathologies of traffic flow • Harmonic fields in extended projective space They also arise in models for the early universe, for cosmic acceleration, and for possible violation of causality in the interiors of certain compact stars. Within the past 25 years, they have become central to the isometric embedding of Riemannian manifolds and the prescription of Gauss curvature for surfaces: topics in pure mathematics which themselves have important applications. Elliptic−Hyperbolic Partial Differential Equations is derived from a mini-course given at the ICMS Workshop on Differential Geometry and Continuum Mechanics held in Edinburgh, Scotland in June 2013. The focus on geometry in that meeting is reflected in these notes, along with the focus on quasilinear equations. In the spirit of the ICMS workshop, this course is addressed both to applied mathematicians and to mathematically-oriented engineers. The emphasis is on very recent applications and methods, the majority of which have not previously appeared in book form.
Publisher: Springer
ISBN: 3319197614
Category : Mathematics
Languages : en
Pages : 134
Book Description
This text is a concise introduction to the partial differential equations which change from elliptic to hyperbolic type across a smooth hypersurface of their domain. These are becoming increasingly important in diverse sub-fields of both applied mathematics and engineering, for example: • The heating of fusion plasmas by electromagnetic waves • The behaviour of light near a caustic • Extremal surfaces in the space of special relativity • The formation of rapids; transonic and multiphase fluid flow • The dynamics of certain models for elastic structures • The shape of industrial surfaces such as windshields and airfoils • Pathologies of traffic flow • Harmonic fields in extended projective space They also arise in models for the early universe, for cosmic acceleration, and for possible violation of causality in the interiors of certain compact stars. Within the past 25 years, they have become central to the isometric embedding of Riemannian manifolds and the prescription of Gauss curvature for surfaces: topics in pure mathematics which themselves have important applications. Elliptic−Hyperbolic Partial Differential Equations is derived from a mini-course given at the ICMS Workshop on Differential Geometry and Continuum Mechanics held in Edinburgh, Scotland in June 2013. The focus on geometry in that meeting is reflected in these notes, along with the focus on quasilinear equations. In the spirit of the ICMS workshop, this course is addressed both to applied mathematicians and to mathematically-oriented engineers. The emphasis is on very recent applications and methods, the majority of which have not previously appeared in book form.
The Dirichlet Problem for Elliptic-Hyperbolic Equations of Keldysh Type
Author: Thomas H. Otway
Publisher: Springer Science & Business Media
ISBN: 3642244149
Category : Mathematics
Languages : en
Pages : 219
Book Description
Partial differential equations of mixed elliptic-hyperbolic type arise in diverse areas of physics and geometry, including fluid and plasma dynamics, optics, cosmology, traffic engineering, projective geometry, geometric variational theory, and the theory of isometric embeddings. And yet even the linear theory of these equations is at a very early stage. This text examines various Dirichlet problems which can be formulated for equations of Keldysh type, one of the two main classes of linear elliptic-hyperbolic equations. Open boundary conditions (in which data are prescribed on only part of the boundary) and closed boundary conditions (in which data are prescribed on the entire boundary) are both considered. Emphasis is on the formulation of boundary conditions for which solutions can be shown to exist in an appropriate function space. Specific applications to plasma physics, optics, and analysis on projective spaces are discussed. (From the preface)
Publisher: Springer Science & Business Media
ISBN: 3642244149
Category : Mathematics
Languages : en
Pages : 219
Book Description
Partial differential equations of mixed elliptic-hyperbolic type arise in diverse areas of physics and geometry, including fluid and plasma dynamics, optics, cosmology, traffic engineering, projective geometry, geometric variational theory, and the theory of isometric embeddings. And yet even the linear theory of these equations is at a very early stage. This text examines various Dirichlet problems which can be formulated for equations of Keldysh type, one of the two main classes of linear elliptic-hyperbolic equations. Open boundary conditions (in which data are prescribed on only part of the boundary) and closed boundary conditions (in which data are prescribed on the entire boundary) are both considered. Emphasis is on the formulation of boundary conditions for which solutions can be shown to exist in an appropriate function space. Specific applications to plasma physics, optics, and analysis on projective spaces are discussed. (From the preface)
Partial Differential Equations and Their Applications
Author: Peter Charles Greiner
Publisher: American Mathematical Soc.
ISBN: 9780821870143
Category : Mathematics
Languages : en
Pages : 332
Book Description
Just list for purposes of NBB.
Publisher: American Mathematical Soc.
ISBN: 9780821870143
Category : Mathematics
Languages : en
Pages : 332
Book Description
Just list for purposes of NBB.
Partial Differential Equations
Author: Bhamra
Publisher: PHI Learning Pvt. Ltd.
ISBN: 8120339177
Category : Mathematics
Languages : en
Pages : 580
Book Description
and postgraduate (MA/MSc) students of mathematics, and conforms to the course curriculum prescribed by UGC. The text is broadly organized into two parts. The first part (Lessons 1 to 15) mostly covers the first-order equations in two variables. In these lessons, the mathematical importance of PDEs of first order in physics and applied sciences has also been highlighted. The other part (Lessons 16 to 50) deals with the various properties of second-order and first- order PDEs. The book emphasizes the applications of PDEs and covers various important topics such as the Hamilton Jacobi equation, Conservation laws, Similarity solution, Asymptotics and Power series solution and many more. The graded problems, the techniques for solving them, and a large number of exercises with hints and answers help students gain the necessary skill and confidence in handling the subject.
Publisher: PHI Learning Pvt. Ltd.
ISBN: 8120339177
Category : Mathematics
Languages : en
Pages : 580
Book Description
and postgraduate (MA/MSc) students of mathematics, and conforms to the course curriculum prescribed by UGC. The text is broadly organized into two parts. The first part (Lessons 1 to 15) mostly covers the first-order equations in two variables. In these lessons, the mathematical importance of PDEs of first order in physics and applied sciences has also been highlighted. The other part (Lessons 16 to 50) deals with the various properties of second-order and first- order PDEs. The book emphasizes the applications of PDEs and covers various important topics such as the Hamilton Jacobi equation, Conservation laws, Similarity solution, Asymptotics and Power series solution and many more. The graded problems, the techniques for solving them, and a large number of exercises with hints and answers help students gain the necessary skill and confidence in handling the subject.