Blow Up In Nonlinear Sobolev Type Equations

Author : A. B. Alʹshin
Publisher : Walter de Gruyter
ISBN 13 : 3110255278
Total Pages : 661 pages
Book Rating : 4.70/5 ( download)

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Download or read book Blow-up in Nonlinear Sobolev Type Equations written by A. B. Alʹshin and published by Walter de Gruyter. This book was released on 2011 with total page 661 pages. Available in PDF, EPUB and Kindle. Book excerpt: The monograph is devoted to the study of initial-boundary-value problems for multi-dimensional Sobolev-type equations over bounded domains. The authors consider both specific initial-boundary-value problems and abstract Cauchy problems for first-order (in the time variable) differential equations with nonlinear operator coefficients with respect to spatial variables. The main aim of the monograph is to obtain sufficient conditions for global (in time) solvability, to obtain sufficient conditions for blow-up of solutions at finite time, and to derive upper and lower estimates for the blow-up time. The abstract results apply to a large variety of problems. Thus, the well-known Benjamin-Bona-Mahony-Burgers equation and Rosenau-Burgers equations with sources and many other physical problems are considered as examples. Moreover, the method proposed for studying blow-up phenomena for nonlinear Sobolev-type equations is applied to equations which play an important role in physics. For instance, several examples describe different electrical breakdown mechanisms in crystal semiconductors, as well as the breakdown in the presence of sources of free charges in a self-consistent electric field. The monograph contains a vast list of references (440 items) and gives an overall view of the contemporary state-of-the-art of the mathematical modeling of various important problems arising in physics. Since the list of references contains many papers which have been published previously only in Russian research journals, it may also serve as a guide to the Russian literature.

Author : Maxim Olegovich Korpusov
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110602075
Total Pages : 344 pages
Book Rating : 4.74/5 ( download)

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Download or read book Blow-Up in Nonlinear Equations of Mathematical Physics written by Maxim Olegovich Korpusov and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-08-06 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present book carefully studies the blow-up phenomenon of solutions to partial differential equations, including many equations of mathematical physics. The included material is based on lectures read by the authors at the Lomonosov Moscow State University, and the book is addressed to a wide range of researchers and graduate students working in nonlinear partial differential equations, nonlinear functional analysis, and mathematical physics. Contents Nonlinear capacity method of S. I. Pokhozhaev Method of self-similar solutions of V. A. Galaktionov Method of test functions in combination with method of nonlinear capacity Energy method of H. A. Levine Energy method of G. Todorova Energy method of S. I. Pokhozhaev Energy method of V. K. Kalantarov and O. A. Ladyzhenskaya Energy method of M. O. Korpusov and A. G. Sveshnikov Nonlinear Schrödinger equation Variational method of L. E. Payne and D. H. Sattinger Breaking of solutions of wave equations Auxiliary and additional results

Author : Olivier Druet
Publisher : Princeton University Press
ISBN 13 : 1400826160
Total Pages : 224 pages
Book Rating : 4.62/5 ( download)

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Download or read book Blow-up Theory for Elliptic PDEs in Riemannian Geometry (MN-45) written by Olivier Druet and published by Princeton University Press. This book was released on 2009-01-10 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: Elliptic equations of critical Sobolev growth have been the target of investigation for decades because they have proved to be of great importance in analysis, geometry, and physics. The equations studied here are of the well-known Yamabe type. They involve Schrödinger operators on the left hand side and a critical nonlinearity on the right hand side. A significant development in the study of such equations occurred in the 1980s. It was discovered that the sequence splits into a solution of the limit equation--a finite sum of bubbles--and a rest that converges strongly to zero in the Sobolev space consisting of square integrable functions whose gradient is also square integrable. This splitting is known as the integral theory for blow-up. In this book, the authors develop the pointwise theory for blow-up. They introduce new ideas and methods that lead to sharp pointwise estimates. These estimates have important applications when dealing with sharp constant problems (a case where the energy is minimal) and compactness results (a case where the energy is arbitrarily large). The authors carefully and thoroughly describe pointwise behavior when the energy is arbitrary. Intended to be as self-contained as possible, this accessible book will interest graduate students and researchers in a range of mathematical fields.

Author : Nakao Hayashi
Publisher : Springer
ISBN 13 : 3540320601
Total Pages : 570 pages
Book Rating : 4.09/5 ( download)

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Download or read book Asymptotics for Dissipative Nonlinear Equations written by Nakao Hayashi and published by Springer. This book was released on 2006-08-23 with total page 570 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book in world literature giving a systematic development of a general asymptotic theory for nonlinear partial differential equations with dissipation. Many typical well-known equations are considered as examples, such as: nonlinear heat equation, KdVB equation, nonlinear damped wave equation, Landau-Ginzburg equation, Sobolev type equations, systems of equations of Boussinesq, Navier-Stokes and others.

Author : Alexey Beskopylny
Publisher : Springer Nature
ISBN 13 : 3031212193
Total Pages : 3148 pages
Book Rating : 4.92/5 ( download)

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Download or read book XV International Scientific Conference “INTERAGROMASH 2022” written by Alexey Beskopylny and published by Springer Nature. This book was released on 2023-02-24 with total page 3148 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book contains proceedings of the XV International Scientific Conference INTERAGROMASH 2022, Rostov-on-Don, Russia. This conference is dedicated to the innovations in the field of precision agriculture, robotics and machines, as well as agriculture biotechnologies and soil management. It is a collection of original and fundamental research in such areas as follows: unmanned aerial systems, satellite-based applications, proximal and remote sensing of soil and crop, positioning systems, geostatistics, mapping and spatial data analysis, robotics, and automation. Potential and prospects for the use of hydrogen in agriculture, for example, in high-performance tractors with hybrid electric transmission, are disclosed in the research works of scientists from all over the world. It also includes such topics as precision horticulture, precision crop protection, differential harvest, precision livestock farming, controlling environment in animal husbandry, and other topics. One of the important issues raised in the book is to ensure the autonomy of local farms. The topic of the impact of the agro-industrial sector on the environment also received wide coverage. Ways to reduce the burden on the environment are proposed, and the use of alternative fuels and fertilizers is suggested. The research results presented in this book cover the experience and the latest studies on the sustainable functioning of agribusiness in several climatic zones. The tundra and taiga, forest-steppe, the steppe and semi-desert—all this is a unique and incredibly demanded bank of information, the main value of which is the real experience of the functioning of agribusiness in difficult climatic and geographic conditions. These materials are of interest for professionals and practitioners, for researchers, scholars, and producers. They are used in the educational process at specific agricultural universities or during vocational training at enterprises and also become an indispensable helper to farm managers in making the best agronomic decisions.

Author : Jacek Banasiak
Publisher : Springer
ISBN 13 : 3319121456
Total Pages : 338 pages
Book Rating : 4.51/5 ( download)

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Download or read book Semigroups of Operators -Theory and Applications written by Jacek Banasiak and published by Springer. This book was released on 2014-11-20 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many results, both from semi group theory itself and from the applied sciences, are phrased in discipline-specific languages and hence are hardly known to a broader community. This volume contains a selection of lectures presented at a conference that was organised as a forum for all mathematicians using semi group theory to learn what is happening outside their own field of research. The collection will help to establish a number of new links between various sub-disciplines of semigroup theory, stochastic processes, differential equations and the applied fields. The theory of semigroups of operators is a well-developed branch of functional analysis. Its foundations were laid at the beginning of the 20th century, while the fundamental generation theorem of Hille and Yosida dates back to the forties. The theory was, from the very beginning, designed as a universal language for partial differential equations and stochastic processes, but at the same time it started to live as an independent branch of operator theory. Nowadays, it still has the same distinctive flavour: it develops rapidly by posing new ‘internal’ questions and in answering them, discovering new methods that can be used in applications. On the other hand, it is influenced by questions from PDEs and stochastic processes as well as from applied sciences such as mathematical biology and optimal control, and thus it continually gathers a new momentum. Researchers and postgraduate students working in operator theory, partial differential equations, probability and stochastic processes, analytical methods in biology and other natural sciences, optimization and optimal control will find this volume useful.

Author : Vitaly Volpert
Publisher : Springer
ISBN 13 : 3034808135
Total Pages : 796 pages
Book Rating : 4.32/5 ( download)

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Download or read book Elliptic Partial Differential Equations written by Vitaly Volpert and published by Springer. This book was released on 2014-05-10 with total page 796 pages. Available in PDF, EPUB and Kindle. Book excerpt: If we had to formulate in one sentence what this book is about, it might be "How partial differential equations can help to understand heat explosion, tumor growth or evolution of biological species". These and many other applications are described by reaction-diffusion equations. The theory of reaction-diffusion equations appeared in the first half of the last century. In the present time, it is widely used in population dynamics, chemical physics, biomedical modelling. The purpose of this book is to present the mathematical theory of reaction-diffusion equations in the context of their numerous applications. We will go from the general mathematical theory to specific equations and then to their applications. Existence, stability and bifurcations of solutions will be studied for bounded domains and in the case of travelling waves. The classical theory of reaction-diffusion equations and new topics such as nonlocal equations and multi-scale models in biology will be considered.

Author : Georgy A. Sviridyuk
Publisher : Walter de Gruyter
ISBN 13 : 3110915502
Total Pages : 224 pages
Book Rating : 4.01/5 ( download)

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Download or read book Linear Sobolev Type Equations and Degenerate Semigroups of Operators written by Georgy A. Sviridyuk and published by Walter de Gruyter. This book was released on 2012-06-04 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focusing on the mathematics, and providing only a minimum of explicatory comment, this volume contains six chapters covering auxiliary material, relatively p-radial operators, relatively p-sectorial operators, relatively σ-bounded operators, Cauchy problems for inhomogenous Sobolev-type equations, bounded solutions to Sobolev-type equations, and optimal control.

Author : Eugene A. Belchev
Publisher :
ISBN 13 :
Total Pages : 116 pages
Book Rating : 4.79/5 ( download)

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Download or read book Finite-time Blow-up of Solutions to Nonlinear Wave Equations written by Eugene A. Belchev and published by . This book was released on 1999 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Olivier Druet
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.08/5 ( download)

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Download or read book Blow-up Theory for Elliptic PDEs in Riemannian Geometry written by Olivier Druet and published by . This book was released on 2009 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: