Songmu Zheng's Books

Boundary Value Problems with Equivalued Surface and Resistivity Well-Logging

By: T Li,Songmu Zheng,Yong-Si Tan,Weixi Shen

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Boundary Value Problems with Equivalued Surface and Resistivity Well-Logging

By: T Li,Songmu Zheng,Yong-Si Tan,Weixi Shen

This first part of this book deals with the boundary value problem with equivalued surfaces, while the second part is concerned with the mathematical model and method, including the numerical method, of the resistivity well-logging for the three-lateral well-logging.

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Page Count

228

Publisher

CRC Press

Published Date

ISBN 10

0582276322

ISBN 13

9780582276321

Nonlinear Parabolic Equations and Hyperbolic-Parabolic Coupled Systems

By: Songmu Zheng

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Nonlinear Parabolic Equations and Hyperbolic-Parabolic Coupled Systems

By: Songmu Zheng

This monograph is devoted to the global existence, uniqueness and asymptotic behaviour of smooth solutions to both initial value problems and initial boundary value problems for nonlinear parabolic equations and hyperbolic parabolic coupled systems. Most of the material is based on recent research carried out by the author and his collaborators. The book can be divided into two parts. In the first part, the results on decay of solutions to nonlinear parabolic equations and hyperbolic parabolic coupled systems are obtained, and a chapter is devoted to the global existence of small smooth solutions to fully nonlinear parabolic equations and quasilinear hyperbolic parabolic coupled systems. Applications of the results to nonlinear thermoelasticity and fluid dynamics are also shown. Some nonlinear parabolic equations and coupled systems arising from the study of phase transitions are investigated in the second part of the book. The global existence, uniqueness and asymptotic behaviour of smooth solutions with arbitrary initial data are obtained. The final chapter is further devoted to related topics: multiplicity of equilibria and the existence of a global attractor, inertial manifold and inertial set. A knowledge of partial differential equations and Sobolev spaces is assumed. As an aid to the reader, the related concepts and results are collected and the relevant references given in the first chapter. The work will be of interest to researchers and graduate students in pure and applied mathematics, mathematical physics and applied sciences.

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Page Count

274

Publisher

CRC Press

Published Date

ISBN 10

1000083241

ISBN 13

9781000083248

Semigroups Associated with Dissipative Systems

By: Z Liu,Songmu Zheng

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Semigroups Associated with Dissipative Systems

By: Z Liu,Songmu Zheng

Motivated by applications to control theory and to the theory of partial differential equations (PDE's), the authors examine the exponential stability and analyticity of C0-semigroups associated with various dissipative systems. They present a unique, systematic approach in which they prove exponential stability by combining a theory from semigroup theory with partial differential equation techniques, and use an analogous theorem with PDE techniques to prove analyticity. The result is a powerful but simple tool useful in determining whether these properties will preserve for a given dissipative system. The authors show that the exponential stability is preserved for all the mechanical systems considered in this book-linear, one-dimensional thermoelastic, viscoelastic and thermoviscoelastic systems, plus systems with shear or friction damping. However, readers also learn that this property does not hold true for linear three-dimensional systems without making assumptions on the domain and initial data, and that analyticity is a more sensitive property, not preserved even for some of the systems addressed in this study.

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Page Count

228

Publisher

CRC Press

Published Date

ISBN 10

0849306159

ISBN 13

9780849306150

Nonlinear Evolution Equations

By: Songmu Zheng

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Nonlinear Evolution Equations

By: Songmu Zheng

Nonlinear evolution equations arise in many fields of sciences including physics, mechanics, and material science. This book introduces some important methods for dealing with these equations and explains clearly and concisely a wide range of relevant theories and techniques. These include the semigroup method, the compactness and monotone operator methods, the monotone iterative method and invariant regions, the global existence and uniqueness theory for small initial data, and the asymptotic behavior of solutions and global attractors. Many of the results are published in book form for the first time. Bibliographic comments in each chapter provide the reader with references and further reading materials to enable further research and study.

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Page Count

302

Publisher

CRC Press

Published Date

ISBN 10

1135436479

ISBN 13

9781135436476

Nonlinear Parabolic Equations and Hyperbolic-Parabolic Coupled Systems

By: Songmu Zheng

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Nonlinear Parabolic Equations and Hyperbolic-Parabolic Coupled Systems

By: Songmu Zheng

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Solve jigsaw puzzle

Age

Page Count

274

Publisher

CRC Press

Published Date

ISBN 10

1000083241

ISBN 13

9781000083248

Book's by Songmu Zheng

Boundary Value Problems with Equivalued Surface and Resistivity Well-Logging

Boundary Value Problems with Equivalued Surface and Resistivity Well-Logging

Nonlinear Parabolic Equations and Hyperbolic-Parabolic Coupled Systems

Nonlinear Parabolic Equations and Hyperbolic-Parabolic Coupled Systems

Semigroups Associated with Dissipative Systems

Semigroups Associated with Dissipative Systems

Nonlinear Evolution Equations

Nonlinear Evolution Equations

Nonlinear Parabolic Equations and Hyperbolic-Parabolic Coupled Systems

Nonlinear Parabolic Equations and Hyperbolic-Parabolic Coupled Systems

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