Mathematical Approach to Nonlinear Phenomena PDF Download
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Author: T. Aiki
Publisher:
ISBN: 9784762504327
Category :
Languages : en
Pages : 327
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Book Description
Author: T. Aiki
Publisher:
ISBN: 9784762504327
Category :
Languages : en
Pages : 327
Get Book Here
Book Description
Author: V. Lakshmikantham
Publisher: Elsevier
ISBN: 1483272052
Category : Mathematics
Languages : en
Pages : 1062
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Book Description
Nonlinear Phenomena in Mathematical Sciences contains the proceedings of an International Conference on Nonlinear Phenomena in Mathematical Sciences, held at the University of Texas at Arlington, on June 16-20,1980. The papers explore trends in nonlinear phenomena in mathematical sciences, with emphasis on nonlinear functional analytic methods and their applications; nonlinear wave theory; and applications to medical and life sciences. In the area of nonlinear functional analytic methods and their applications, the following subjects are discussed: optimal control theory; periodic oscillations of nonlinear mechanical systems; Leray-Schauder degree theory; differential inequalities applied to parabolic and elliptic partial differential equations; bifurcation theory, stability theory in analytical mechanics; singular and ordinary boundary value problems, etc. The following topics in nonlinear wave theory are considered: nonlinear wave propagation in a randomly homogeneous media; periodic solutions of a semilinear wave equation; asymptotic behavior of solutions of strongly damped nonlinear wave equations; shock waves and dissipation theoretical methods for a nonlinear Schr?dinger equation; and nonlinear hyperbolic Volterra equations occurring in viscoelasticity. Applications to medical and life sciences include mathematical modeling in physiology, pharmacokinetics, and neuro-mathematics, along with epidemic modeling and parameter estimation techniques. This book will be helpful to students, practitioners, and researchers in the field of mathematics.
Author: Victoriano Carmona
Publisher: Springer
ISBN: 3319667661
Category : Science
Languages : en
Pages : 424
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Book Description
This book is part of a two volume set which presents the analysis of nonlinear phenomena as a long-standing challenge for research in basic and applied science as well as engineering. It discusses nonlinear differential and differential equations, bifurcation theory for periodic orbits and global connections. The integrability and reversibility of planar vector fields and theoretical analysis of classic physical models are sketched. This first volume concentrates on the mathematical theory and computational techniques that are essential for the study of nonlinear science, a second volume deals with real-world nonlinear phenomena in condensed matter, biology and optics.
Author: J. A. Tenreiro Machado
Publisher: Springer Nature
ISBN: 3030371417
Category : Mathematics
Languages : en
Pages : 231
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Book Description
This collection covers new aspects of numerical methods in applied mathematics, engineering, and health sciences. It provides recent theoretical developments and new techniques based on optimization theory, partial differential equations (PDEs), mathematical modeling and fractional calculus that can be used to model and understand complex behavior in natural phenomena. Specific topics covered in detail include new numerical methods for nonlinear partial differential equations, global optimization, unconstrained optimization, detection of HIV- Protease, modelling with new fractional operators, analysis of biological models, and stochastic modelling.
Author: Andrei Ludu
Publisher: MDPI
ISBN: 3039287265
Category : Mathematics
Languages : en
Pages : 122
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Book Description
Nonlinear science is the science of, among other exotic phenomena, unexpected and unpredictable behavior, catastrophes, complex interactions, and significant perturbations. Ocean and atmosphere dynamics, weather, many bodies in interaction, ultra-high intensity excitations, life, formation of natural patterns, and coupled interactions between components or different scales are only a few examples of systems where nonlinear science is necessary. All outstanding, self-sustained, and stable structures in space and time exist and protrude out of a regular linear background of states mainly because they identify themselves from the rest by being highly localized in range, time, configuration, states, and phase spaces. Guessing how high up you drive toward the top of the mountain by compiling your speed, road slope, and trip duration is a linear model, but predicting the occurrence around a turn of a boulder fallen on the road is a nonlinear phenomenon. In an effort to grasp and understand nonlinear phenomena, scientists have developed several mathematical approaches including inverse scattering theory, Backlund and groups of transformations, bilinear method, and several other detailed technical procedures. In this Special Issue, we introduce a few very recent approaches together with their physical meaning and applications. We present here five important papers on waves, unsteady flows, phases separation, ocean dynamics, nonlinear optic, viral dynamics, and the self-appearance of patterns for spatially extended systems, which are problems that have aroused scientists’ interest for decades, yet still cannot be predicted and have their generating mechanism and stability open to debate. The aim of this Special Issue was to present these most debated and interesting topics from nonlinear science for which, despite the existence of highly developed mathematical tools of investigation, there are still fundamental open questions.
Author: V. Benci
Publisher: Springer Science & Business Media
ISBN: 1461200814
Category : Mathematics
Languages : en
Pages : 133
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Book Description
This volume covers recent advances in the field of nonlinear functional analysis and its applications to nonlinear partial and ordinary differential equations, with particular emphasis on variational and topological methods. A broad range of topics is covered, including: * concentration phenomena in pdes * variational methods with applications to pdes and physics * periodic solutions of odes * computational aspects in topological methods * mathematical models in biology Though well-differentiated, the topics covered are unified through a common perspective and approach. Unique to the work are several chapters on computational aspects and applications to biology, not usually found with such basic studies on pdes and odes. The volume is an excellent reference text for researchers and graduate students in the above mentioned fields. Contributors: M. Clapp, M. Del Pino, M.J. Esteban, P. Felmer, A. Ioffe, W. Marzantowicz, M. Mrozek, M. Musso, R. Ortega, P. Pilarczyk, E. Séré, E. Schwartzman, P. Sintzoff, R. Turner , M. Willem.
Author: Angela Slavova
Publisher: Cambridge Scholars Publishing
ISBN: 1527507351
Category : Mathematics
Languages : en
Pages : 220
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Book Description
This book presents a study of neuroscience models and natural phenomena, such as tsunami waves and tornados. The first part discusses various mathematical models of tsunamis, including the Korteweg–de Vries equation, shallow water equations and the Camassa–Holm equation (CH). In order to study the dynamics of these models, the text uses the Cellular Nonlinear Networks (CNN) approach to discretize the governing equation using a suitable mathematical grid. The second part discusses some of the models arising in the field of neuroscience. It examines the Fitzhugh-Nagumo systems, which are very important for understanding the qualitative nature of nerve impulse propagation. The volume will be of interest to a wide-ranging audience, including PhD students, mathematicians, physicists, engineers and specialists in the domain of nonlinear waves and their applications.
Author: Robin Kaiser
Publisher: World Scientific
ISBN: 9814493007
Category : Science
Languages : en
Pages : 296
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Book Description
Nonlinear science has a very broad scope and the aim of this volume of lectures is to introduce different aspects of this vast domain to research students whose studies are necessarily concentrated on only one. The lectures given at summer schools in France between 1997 and 1999, describe analytical, geometrical and experimental approaches to subjects as diverse as turbulence, elasticity, physiology, classical mechanics, quantum chaos, water waves and the laser cooling of atoms.
Author: A.N. Proto
Publisher: Elsevier
ISBN: 0444598758
Category : Science
Languages : en
Pages : 264
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Book Description
This book contains a thorough treatment of neural networks, cellular-automata and synergetics, in an attempt to provide three different approaches to nonlinear phenomena in complex systems. These topics are of major interest to physicists active in the fields of statistical mechanics and dynamical systems. They have been developed with a high degree of sophistication and include the refinements necessary to work with the complexity of real systems as well as the more recent research developments in these areas.
Author: Yasunori Maekawa
Publisher: Springer
ISBN: 3319667645
Category : Mathematics
Languages : en
Pages : 335
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Book Description
This volume covers some of the most seminal research in the areas of mathematical analysis and numerical computation for nonlinear phenomena. Collected from the international conference held in honor of Professor Yoshikazu Giga’s 60th birthday, the featured research papers and survey articles discuss partial differential equations related to fluid mechanics, electromagnetism, surface diffusion, and evolving interfaces. Specific focus is placed on topics such as the solvability of the Navier-Stokes equations and the regularity, stability, and symmetry of their solutions, analysis of a living fluid, stochastic effects and numerics for Maxwell’s equations, nonlinear heat equations in critical spaces, viscosity solutions describing various kinds of interfaces, numerics for evolving interfaces, and a hyperbolic obstacle problem. Also included in this volume are an introduction of Yoshikazu Giga’s extensive academic career and a long list of his published work. Students and researchers in mathematical analysis and computation will find interest in this volume on theoretical study for nonlinear phenomena.
