Download or read book Linear and Nonlinear Perturbations of the Operator Div written by Viktor Grigorʹevich Osmolovskiĭ and published by American Mathematical Soc.. This book was released on 1997-01-01 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents results onboundary-value problems for L and the theory of nonlinear perturbations of L. Specifically, necessary and sufficient solvability conditions in explicit form are found for various boundary-value problems for the operator L. an analog of the Weyl decomposition is proved.

Download or read book Linear and Nonlinear Perturbation of the Operator Div written by V. G. Osmolovskii and published by . This book was released on 1997 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Linear and Nonlinear Perturbations of the Operator Div written by Viktor Grigorʹevich Osmolovskiĭ and published by American Mathematical Soc.. This book was released on 1997 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: The perturbation theory for the operator div is of particular interest in the study of boundary-value problems for the general nonlinear equation $F(\dot y,y,x)=0$. Taking as linearization the first order operator $Lu=C_{ij}u_{x_j}^i+C_iu^i$, one can, under certain conditions, regard the operator $L$ as a compact perturbation of the operator div. This book presents results on boundary-value problems for $L$ and the theory of nonlinear perturbations of $L$. Specifically, necessary and sufficient solvability conditions in explicit form are found for various boundary-value problems for the operator $L$. An analog of the Weyl decomposition is proved. The book also contains a local description of the set of all solutions (located in a small neighborhood of a known solution) to the boundary-value problems for the nonlinear equation $F(\dot y, y, x) = 0$ for which $L$ is a linearization. A classification of sets of all solutions to various boundary-value problems for the nonlinear equation $F(\dot y, y, x) = 0$ is given. The results are illustrated by various applications in geometry, the calculus of variations, physics, and continuum mechanics.

Download or read book Linear and Nonlinear Perturbations of the Operator Operatorname div written by Viktor Grigorʹevich Osmolovskiĭ and published by . This book was released on 1997 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt: The perturbation theory for the operator div is of particular interest in the study of boundary-value problems for the general nonlinear equation F(\dot y, y, x)=0. Taking as linearization the first order operator Lu=C_{ij}u_{x_j}^i+C_iu^i, one can, under certain conditions, regard the operator L as a compact perturbation of the operator div. This book presents results on boundary-value problems for L and the theory of nonlinear perturbations of L. Specifically, necessary and sufficient solvability conditions in explicit form are found for various boundary-value problems for the operator L. An a.

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Download or read book Wavelet Methods for Solving Partial Differential Equations and Fractional Differential Equations written by Santanu Saha Ray and published by CRC Press. This book was released on 2018-01-12 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main focus of the book is to implement wavelet based transform methods for solving problems of fractional order partial differential equations arising in modelling real physical phenomena. It explores analytical and numerical approximate solution obtained by wavelet methods for both classical and fractional order partial differential equations.

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Download or read book Abstracts of Papers Presented to the American Mathematical Society written by American Mathematical Society and published by . This book was released on 1997 with total page 658 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Partial Differential Equations written by Abdelmoujib Benkirane and published by CRC Press. This book was released on 2002-05-06 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: This impressive compilation of the material presented at the International Conference on Partial Differential Equations held in Fez, Morocco, represents an integrated discussion of all major topics in the area of partial differential equations--highlighting recent progress and new trends for real-world applications.

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Download or read book Shocks Singularities and Oscillations in Nonlinear Optics and Fluid Mechanics written by Ferruccio Colombini and published by Springer. This book was released on 2017-04-25 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book collects the most relevant results from the INdAM Workshop "Shocks, Singularities and Oscillations in Nonlinear Optics and Fluid Mechanics" held in Rome, September 14-18, 2015. The contributions discuss recent major advances in the study of nonlinear hyperbolic systems, addressing general theoretical issues such as symmetrizability, singularities, low regularity or dispersive perturbations. It also investigates several physical phenomena where such systems are relevant, such as nonlinear optics, shock theory (stability, relaxation) and fluid mechanics (boundary layers, water waves, Euler equations, geophysical flows, etc.). It is a valuable resource for researchers in these fields.

Download or read book Enabling Technologies for High Spectral efficiency Coherent Optical Communication Networks written by Xiang Zhou and published by John Wiley & Sons. This book was released on 2016-04-29 with total page 719 pages. Available in PDF, EPUB and Kindle. Book excerpt: Enabling Technologies for High Spectral-efficiency Coherent Optical Communication Networks Presents the technological advancements that enable high spectral-efficiency and high-capacity fiber-optic communication systems and networks This book examines key technology advances in high spectral-efficiency fiber-optic communication systems and networks, enabled by the use of coherent detection and digital signal processing (DSP). The first of this book’s 16 chapters is a detailed introduction. Chapter 2 reviews the modulation formats, while Chapter 3 focuses on detection and error correction technologies for coherent optical communication systems. Chapters 4 and 5 are devoted to Nyquist-WDM and orthogonal frequency-division multiplexing (OFDM). In chapter 6, polarization and nonlinear impairments in coherent optical communication systems are discussed. The fiber nonlinear effects in a non-dispersion-managed system are covered in chapter 7. Chapter 8 describes linear impairment equalization and Chapter 9 discusses various nonlinear mitigation techniques. Signal synchronization is covered in Chapters 10 and 11. Chapter 12 describes the main constraints put on the DSP algorithms by the hardware structure. Chapter 13 addresses the fundamental concepts and recent progress of photonic integration. Optical performance monitoring and elastic optical network technology are the subjects of Chapters 14 and 15. Finally, Chapter 16 discusses spatial-division multiplexing and MIMO processing technology, a potential solution to solve the capacity limit of single-mode fibers. Contains basic theories and up-to-date technology advancements in each chapter Describes how capacity-approaching coding schemes based on low-density parity check (LDPC) and spatially coupled LDPC codes can be constructed by combining iterative demodulation and decoding Demonstrates that fiber nonlinearities can be accurately described by some analytical models, such as GN-EGN model Presents impairment equalization and mitigation techniques Enabling Technologies for High Spectral-efficiency Coherent Optical Communication Networks is a reference for researchers, engineers, and graduate students.