Beyond Partial Differential Equations
Beyond Partial Differential Equations

Author: Horst Reinhard Beyer

Publisher: Springer

Published: 2007-04-10

Total Pages: 291

ISBN-13: 3540711295

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This book introduces the treatment of linear and nonlinear (quasi-linear) abstract evolution equations by methods from the theory of strongly continuous semigroups. The theoretical part is accessible to graduate students with basic knowledge in functional analysis, with only some examples requiring more specialized knowledge from the spectral theory of linear, self-adjoint operators in Hilbert spaces. Emphasis is placed on equations of the hyperbolic type which are less often treated in the literature.

Introduction to Partial Differential Equations with Applications
Introduction to Partial Differential Equations with Applications

Author: E. C. Zachmanoglou

Publisher: Courier Corporation

Published: 2012-04-20

Total Pages: 434

ISBN-13: 048613217X

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This text explores the essentials of partial differential equations as applied to engineering and the physical sciences. Discusses ordinary differential equations, integral curves and surfaces of vector fields, the Cauchy-Kovalevsky theory, more. Problems and answers.

Hyperbolic Partial Differential Equations
Hyperbolic Partial Differential Equations

Author: Serge Alinhac

Publisher: Springer Science & Business Media

Published: 2009-06-17

Total Pages: 159

ISBN-13: 0387878238

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This excellent introduction to hyperbolic differential equations is devoted to linear equations and symmetric systems, as well as conservation laws. The book is divided into two parts. The first, which is intuitive and easy to visualize, includes all aspects of the theory involving vector fields and integral curves; the second describes the wave equation and its perturbations for two- or three-space dimensions. Over 100 exercises are included, as well as "do it yourself" instructions for the proofs of many theorems. Only an understanding of differential calculus is required. Notes at the end of the self-contained chapters, as well as references at the end of the book, enable ease-of-use for both the student and the independent researcher.

Theory and Application of Hyperbolic Systems of Quasilinear Equations
Theory and Application of Hyperbolic Systems of Quasilinear Equations

Author: Hyun-Ku Rhee

Publisher: Courier Corporation

Published: 2001-01-01

Total Pages: 582

ISBN-13: 9780486419947

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Second volume of a 2-volume set examines physical systems that can usefully be modeled by equations of the first order. The book begins with a consideration of pairs of quasilinear hyperbolic equations of the first order and goes on to explore multicomponent chromatography, complications of counter-current moving-bed adsorbers, more. Exercises. 1989 edition. 198 black-and-white illustrations. Author and subject indices.

Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves
Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves

Author: Peter D. Lax

Publisher: SIAM

Published: 1973-01-01

Total Pages: 55

ISBN-13: 0898711770

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This book deals with the mathematical side of the theory of shock waves. The author presents what is known about the existence and uniqueness of generalized solutions of the initial value problem subject to the entropy conditions. The subtle dissipation introduced by the entropy condition is investigated and the slow decay in signal strength it causes is shown.

First-Order Partial Differential Equations, Vol. 1
First-Order Partial Differential Equations, Vol. 1

Author: Hyun-Ku Rhee

Publisher: Courier Corporation

Published: 2014-05-05

Total Pages: 561

ISBN-13: 0486146200

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This first volume of a highly regarded two-volume text is fully usable on its own. After going over some of the preliminaries, the authors discuss mathematical models that yield first-order partial differential equations; motivations, classifications, and some methods of solution; linear and semilinear equations; chromatographic equations with finite rate expressions; homogeneous and nonhomogeneous quasilinear equations; formation and propagation of shocks; conservation equations, weak solutions, and shock layers; nonlinear equations; and variational problems. Exercises appear at the end of most sections. This volume is geared to advanced undergraduates or first-year grad students with a sound understanding of calculus and elementary ordinary differential equations. 1986 edition. 189 black-and-white illustrations. Author and subject indices.