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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: V. Lakshmikantham
Publisher: Elsevier
ISBN: 1483272052
Category : Mathematics
Languages : en
Pages : 1062
Get Book Here
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: K. W. Chang
Publisher: Springer Science & Business Media
ISBN: 146121114X
Category : Mathematics
Languages : en
Pages : 191
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Book Description
Our purpose in writing this monograph is twofold. On the one hand, we want to collect in one place many of the recent results on the exist ence and asymptotic behavior of solutions of certain classes of singularly perturbed nonlinear boundary value problems. On the other, we hope to raise along the way a number of questions for further study, mostly ques tions we ourselves are unable to answer. The presentation involves a study of both scalar and vector boundary value problems for ordinary dif ferential equations, by means of the consistent use of differential in equality techniques. Our results for scalar boundary value problems obeying some type of maximum principle are fairly complete; however, we have been unable to treat, under any circumstances, problems involving "resonant" behavior. The linear theory for such problems is incredibly complicated already, and at the present time there appears to be little hope for any kind of general nonlinear theory. Our results for vector boundary value problems, even those admitting higher dimensional maximum principles in the form of invariant regions, are also far from complete. We offer them with some trepidation, in the hope that they may stimulate further work in this challenging and important area of differential equa tions. The research summarized here has been made possible by the support over the years of the National Science Foundation and the National Science and Engineering Research Council.
Author: J. A. Tenreiro Machado
Publisher: Springer
ISBN: 9783030371432
Category : Mathematics
Languages : en
Pages : 0
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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: Marius Ghergu
Publisher: Springer Science & Business Media
ISBN: 3642226647
Category : Mathematics
Languages : en
Pages : 402
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Book Description
The emphasis throughout the present volume is on the practical application of theoretical mathematical models helping to unravel the underlying mechanisms involved in processes from mathematical physics and biosciences. It has been conceived as a unique collection of abstract methods dealing especially with nonlinear partial differential equations (either stationary or evolutionary) that are applied to understand concrete processes involving some important applications related to phenomena such as: boundary layer phenomena for viscous fluids, population dynamics,, dead core phenomena, etc. It addresses researchers and post-graduate students working at the interplay between mathematics and other fields of science and technology and is a comprehensive introduction to the theory of nonlinear partial differential equations and its main principles also presents their real-life applications in various contexts: mathematical physics, chemistry, mathematical biology, and population genetics. Based on the authors' original work, this volume provides an overview of the field, with examples suitable for researchers but also for graduate students entering research. The method of presentation appeals to readers with diverse backgrounds in partial differential equations and functional analysis. Each chapter includes detailed heuristic arguments, providing thorough motivation for the material developed later in the text. The content demonstrates in a firm way that partial differential equations can be used to address a large variety of phenomena occurring in and influencing our daily lives. The extensive reference list and index make this book a valuable resource for researchers working in a variety of fields and who are interested in phenomena modeled by nonlinear partial differential equations.
Author: Michael E. Taylor
Publisher: Springer Science & Business Media
ISBN: 1441970495
Category : Mathematics
Languages : en
Pages : 734
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Book Description
The third of three volumes on partial differential equations, this is devoted to nonlinear PDE. It treats a number of equations of classical continuum mechanics, including relativistic versions, as well as various equations arising in differential geometry, such as in the study of minimal surfaces, isometric imbedding, conformal deformation, harmonic maps, and prescribed Gauss curvature. In addition, some nonlinear diffusion problems are studied. It also introduces such analytical tools as the theory of L Sobolev spaces, H lder spaces, Hardy spaces, and Morrey spaces, and also a development of Calderon-Zygmund theory and paradifferential operator calculus. The book is aimed at graduate students in mathematics, and at professional mathematicians with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis and complex analysis
Author: Tönu Puu
Publisher: Springer Science & Business Media
ISBN: 3540246991
Category : Mathematics
Languages : en
Pages : 556
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Book Description
Attractors, Bifurcations, & Chaos - now in its second edition - begins with an introduction to mathematical methods in modern nonlinear dynamics and deals with differential equations. Phenomena such as bifurcations and deterministic chaos are given considerable emphasis, both in the methodological part, and in the second part, containing various applications in economics and in regional science. Coexistence of attractors and the multiplicity of development paths in nonlinear systems are central topics. The applications focus on issues such as business cycles, oligopoly, interregional trade dynamics, and economic development theory.
Author: Catherine Sulem
Publisher: Springer Science & Business Media
ISBN: 0387227687
Category : Mathematics
Languages : en
Pages : 363
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Book Description
Filling the gap between the mathematical literature and applications to domains, the authors have chosen to address the problem of wave collapse by several methods ranging from rigorous mathematical analysis to formal aymptotic expansions and numerical simulations.
Author: Joshua M. Epstein
Publisher: CRC Press
ISBN: 0429973039
Category : Mathematics
Languages : en
Pages : 132
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Book Description
This book is based on a series of lectures on mathematical biology, the essential dynamics of complex and crucially important social systems, and the unifying power of mathematics and nonlinear dynamical systems theory.
Author: Vangipuram Lakshmikantham
Publisher:
ISBN: 9780124341708
Category :
Languages : en
Pages : 1035
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Book Description
Nonlinear Phenomena in Mathematical Sciences ...
Author: Kuppalapalle Vajravelu
Publisher: Springer Science & Business Media
ISBN: 364232102X
Category : Mathematics
Languages : en
Pages : 197
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Book Description
Since most of the problems arising in science and engineering are nonlinear, they are inherently difficult to solve. Traditional analytical approximations are valid only for weakly nonlinear problems and often fail when used for problems with strong nonlinearity. “Nonlinear Flow Phenomena and Homotopy Analysis: Fluid Flow and Heat Transfer” presents the current theoretical developments of the analytical method of homotopy analysis. This book not only addresses the theoretical framework for the method, but also gives a number of examples of nonlinear problems that have been solved by means of the homotopy analysis method. The particular focus lies on fluid flow problems governed by nonlinear differential equations. This book is intended for researchers in applied mathematics, physics, mechanics and engineering. Both Kuppalapalle Vajravelu and Robert A. Van Gorder work at the University of Central Florida, USA.
