This second volume continues the study on asymptotic convergence of global solutions of parabolic equations to stationary solutions by utilizing the theory of abstract parabolic evolution equations and the Łojasiewicz–Simon gradient inequality. In the first volume of the same title, after setting the abstract frameworks of arguments, a general convergence theorem was proved under the four structural assumptions of critical condition, Lyapunov function, angle condition, and gradient inequality. In this volume, with those abstract results reviewed briefly, their applications to concrete parabolic equations are described. Chapter 3 presents a discussion of semilinear parabolic equations of second order in general n-dimensional spaces, and Chapter 4 is devoted to treating epitaxial growth equations of fourth order, which incorporate general roughening functions. In Chapter 5 consideration is given to the Keller–Segel equations in one-, two-, and three-dimensional spaces. Some of these results had already been obtained and published by the author in collaboration with his colleagues. However, by means of the abstract theory described in the first volume, those results can be extended much more. Readers of this monograph should have a standard-level knowledge of functional analysis and of function spaces. Familiarity with functional analytic methods for partial differential equations is also assumed.
The classical Łojasiewicz gradient inequality (1963) was extended by Simon (1983) to the infinite-dimensional setting, now called the Łojasiewicz–Simon gradient inequality. This book presents a unified method to show asymptotic convergence of solutions to a stationary solution for abstract parabolic evolution equations of the gradient form by utilizing this Łojasiewicz–Simon gradient inequality. In order to apply the abstract results to a wider class of concrete nonlinear parabolic equations, the usual Łojasiewicz–Simon inequality is extended, which is published here for the first time. In the second version, these abstract results are applied to reaction–diffusion equations with discontinuous coefficients, reaction–diffusion systems, and epitaxial growth equations. The results are also applied to the famous chemotaxis model, i.e., the Keller–Segel equations even for higher-dimensional ones.
This work presents a detailed study of linear abstract degenerate differential equations, using both the semigroups generated by multivalued (linear) operators and extensions of the operational method from Da Prato and Grisvard. The authors describe the recent and original results on PDEs and algebraic-differential equations, and establishes the an
This monograph is intended to present the fundamentals of the theory of abstract parabolic evolution equations and to show how to apply to various nonlinear dif- sion equations and systems arising in science. The theory gives us a uni?ed and s- tematic treatment for concrete nonlinear diffusion models. Three main approaches are known to the abstract parabolic evolution equations, namely, the semigroup methods, the variational methods, and the methods of using operational equations. In order to keep the volume of the monograph in reasonable length, we will focus on the semigroup methods. For other two approaches, see the related references in Bibliography. The semigroup methods, which go back to the invention of the analytic se- groups in the middle of the last century, are characterized by precise formulas representing the solutions of the Cauchy problem for evolution equations. The ?tA analytic semigroup e generated by a linear operator ?A provides directly a fundamental solution to the Cauchy problem for an autonomous linear e- dU lution equation, +AU =F(t), 0
The classical ojasiewicz gradient inequality (1963) was extended by Simon (1983) to the infinite-dimensional setting, now called the ojasiewiczSimon gradient inequality. This book presents a unified method to show asymptotic convergence of solutions to a stationary solution for abstract parabolic evolution equations of the gradient form by utilizing this ojasiewiczSimon gradient inequality. In order to apply the abstract results to a wider class of concrete nonlinear parabolic equations, the usual ojasiewiczSimon inequality is extended, which is published here for the first time. In the second version, these abstract results are applied to reactiondiffusion equations with discontinuous coefficients, reactiondiffusion systems, and epitaxial growth equations. The results are also applied to the famous chemotaxis model, i.e., the KellerSegel equations even for higher-dimensional ones.
This work presents a detailed study of linear abstract degenerate differential equations, using both the semigroups generated by multivalued (linear) operators and extensions of the operational method from Da Prato and Grisvard. The authors describe the recent and original results on PDEs and algebraic-differential equations, and establishes the analyzability of the semigroup generated by some degenerate parabolic operators in spaces of continuous functions.
This monograph is intended to present the fundamentals of the theory of abstract parabolic evolution equations and to show how to apply to various nonlinear dif- sion equations and systems arising in science. The theory gives us a uni?ed and s- tematic treatment for concrete nonlinear diffusion models. Three main approaches are known to the abstract parabolic evolution equations, namely, the semigroup methods, the variational methods, and the methods of using operational equations. In order to keep the volume of the monograph in reasonable length, we will focus on the semigroup methods. For other two approaches, see the related references in Bibliography. The semigroup methods, which go back to the invention of the analytic se- groups in the middle of the last century, are characterized by precise formulas representing the solutions of the Cauchy problem for evolution equations. The ?tA analytic semigroup e generated by a linear operator ?A provides directly a fundamental solution to the Cauchy problem for an autonomous linear e- dU lution equation, +AU =F(t), 0
This brief is concerned with the fundamentals of corrosion of metallic materials and electrochemistry for better understanding of corrosion phenomena. Corrosion is related to both the environment and material properties, induced by electrochemical reactions at the interface between metallic materials and the environment as in aqueous and gaseous phases. In order to understand corrosion phenomena, knowledge of electrochemistry is thus required, and to investigate the cause of corrosion damage, appropriate electrochemical experiments must be performed. Corrosion scientists should therefore possess knowledge of both electrochemistry and its related experimental techniques. In this book, corrosion phenomena are introduced from the electrochemical aspect. Electrochemical techniques for the study of corrosion are then described with other techniques that can be combined with electrochemistry. Because this brief is characterized as starting with the fundamentals of corrosion and electrochemistry, it is accessible to undergraduate students as well as to graduate students who are beginning corrosion research.
Updated topics in minimally invasive abdominal surgery provides surgeons interested in minimally invasive abdominal surgery with the most recent techniques and discussions in laparoscopic surgery. This book includes different topics covering a big variety of medical conditions with up-to-date information. It discusses many controversies in a clear and user-friendly manner. This book is made for young junior surgeons in training and also senior surgeons who need to know the most recent work in the field of laparoscopy. To make the material easily digestive, we provided the book with many figures and illustrations for different procedures and technical pearls.
The World of Nano-Biomechanics, Second Edition, focuses on the remarkable progress in the application of force spectroscopy to molecular and cellular biology that has occurred since the book's first edition in 2008. The initial excitement of seeing and touching a single molecule of protein/DNA is now culminating in the development of various ways to manipulate molecules and cells almost at our fingertips, enabling live cell operations. Topics include the development of molecular biosensors, mechanical diagnosis, cellular-level wound healing, and a look into the advances that have been made in our understanding of the significance of mechanical rigidity/flexibility of protein/DNA structure for the manifestation of biological activities. The book begins with a summary of the results of basic mechanics to help readers who are unfamiliar with engineering mechanics. Then, representative results obtained on biological macromolecules and structures, such as proteins, DNA, RNA, polysaccharides, lipid membranes, subcellular organelles, and live cells are discussed. New to this second edition are recent developments in three important applications, i.e., advanced AFM-data analysis, high-resolution mechanical biosensing, and the use of cell mechanics for medical diagnosis. Explains the basic physical concepts and mathematics of elementary mechanics needed to understand and perform experimental work on small-scale biological samples Presents recent developments of force-based biosensing Includes novel applications of nano-biomechanics to the medical field
For more than 40 years, pattern recognition approaches are continuingly improving and have been used in an increasing number of areas with great success. This book discloses recent advances and new ideas in approaches and applications for pattern recognition. The 30 chapters selected in this book cover the major topics in pattern recognition. These chapters propose state-of-the-art approaches and cutting-edge research results. I could not thank enough to the contributions of the authors. This book would not have been possible without their support.
This book examines how the Cambridge School economists, such as J. M. Keynes, constructed revolutionary theories and advocated drastic policies based on their ideals for social organizations and their personal characteristics. Although vast numbers of studies on Marshall, Keynes and Marshallians have been published, there have been very few studies on the ‘Keynesian Revolution’ or Keynes’s relevance to the modern world from archival and intellectual viewpoints which focus on Keynes as a member of the Cambridge School. This book approaches Keynes from three directions: person, time and perspective. The book provides a better understanding of how Keynes struggled with problems of his time and it also offers valuable lessons on how to survive fluctuating global capitalism today. It focuses on eight key economists as a group in ‘a public sphere’ rather than as a school (a unified theoretical denominator), and clarifies their visions and the widespread beliefs at the time by investigating their common motivations, lifestyles, values and habits.
Extensive studies of high-Tc cuprate superconductors have stimualted investigations into various transition-metal oxides. Mott transitions in particular provide fascinating problems and new concepts in condensed matter physics. This book is a collection of overviews by well-known, active researchers in this field. It deals with the latest developments, with particular emphasis on the theoretical, spectroscopic, and transport aspects.
Takigi Oze, detective in the army's Criminal Investigation Division and brother to Company 8's own Maki, investigates a case that takes him into the Nether. When he almost doesn't make it out alive, his father--the general--decides it's time for the army to do something about the Evangelist. The general enlists the help of the Special Fire Force, but adds one more demand: Maki must return to the military.
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