Parabolic Equations In Biology PDF Download
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| Author | : Benoît Perthame |
| Publisher | : Springer |
| Total Pages | : 204 |
| Release | : 2015-09-09 |
| Genre | : Mathematics |
| ISBN | : 331919500X |
Download Parabolic Equations in Biology Book in PDF, ePub and Kindle
This book presents several fundamental questions in mathematical biology such as Turing instability, pattern formation, reaction-diffusion systems, invasion waves and Fokker-Planck equations. These are classical modeling tools for mathematical biology with applications to ecology and population dynamics, the neurosciences, enzymatic reactions, chemotaxis, invasion waves etc. The book presents these aspects from a mathematical perspective, with the aim of identifying those qualitative properties of the models that are relevant for biological applications. To do so, it uncovers the mechanisms at work behind Turing instability, pattern formation and invasion waves. This involves several mathematical tools, such as stability and instability analysis, blow-up in finite time, asymptotic methods and relative entropy properties. Given the content presented, the book is well suited as a textbook for master-level coursework.
| Author | : Benoît Perthame |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 206 |
| Release | : 2006-12-14 |
| Genre | : Science |
| ISBN | : 3764378425 |
Download Transport Equations in Biology Book in PDF, ePub and Kindle
This book presents models written as partial differential equations and originating from various questions in population biology, such as physiologically structured equations, adaptive dynamics, and bacterial movement. Its purpose is to derive appropriate mathematical tools and qualitative properties of the solutions. The book further contains many original PDE problems originating in biosciences.
| Author | : Atsushi Yagi |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 594 |
| Release | : 2009-11-03 |
| Genre | : Mathematics |
| ISBN | : 3642046312 |
Download Abstract Parabolic Evolution Equations and their Applications Book in PDF, ePub and Kindle
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
| Author | : C.V. Pao |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 814 |
| Release | : 1992 |
| Genre | : Mathematics |
| ISBN | : 9780306443435 |
Download Nonlinear Parabolic and Elliptic Equations Book in PDF, ePub and Kindle
The recent development of reaction diffusion systems in biology, ecology and biochemistry, and the traditional importance of these systems in physics, heat-mass transfer, and engineering lead to extensive study in nonlinear parabolic and elliptical partial differential equations. This text provides an introduction to the subject as well as applicat.
| Author | : N. F. Britton |
| Publisher | : |
| Total Pages | : 296 |
| Release | : 1986 |
| Genre | : Science |
| ISBN | : |
Download Reaction-diffusion Equations and Their Applications to Biology Book in PDF, ePub and Kindle
Although the book is largely self-contained, some knowledge of the mathematics of differential equations is necessary. Thus the book is intended for mathematicians who are interested in the application of their subject to the biological sciences and for biologists with some mathematical training. It is also suitable for postgraduate mathematics students and for undergraduate mathematicians taking a course in mathematical biology. Increasing use of mathematics in developmental biology, ecology, physiology, and many other areas in the biological sciences has produced a need for a complete, mathematical reference for laboratory practice. In this volume, biological scientists will find a rich resource of interesting applications and illustrations of various mathematical techniques that can be used to analyze reaction-diffusion systems. Concepts covered here include:**systems of ordinary differential equations**conservative systems**the scalar reaction-diffusion equation**analytic techniques for systems of parabolic partial differential equations**bifurcation theory**asymptotic methods for oscillatory systems**singular perturbations**macromolecular carriers -- asymptotic techniques.
| Author | : Atsushi Yagi |
| Publisher | : |
| Total Pages | : 581 |
| Release | : 2009 |
| Genre | : Differential equations, Parabolic |
| ISBN | : 9783642046599 |
Download Abstract Parabolic Evolution Equations and Their Applications Book in PDF, ePub and Kindle
The semigroup methods are known as a powerful tool for analyzing nonlinear diffusion equations and systems. The author has studied abstract parabolic evolution equations and their applications to nonlinear diffusion equations and systems for more than 30 years. He gives first, after reviewing the theory of analytic semigroups, an overview of the theories of linear, semilinear and quasilinear abstract parabolic evolution equations as well as general strategies for constructing dynamical systems, attractors and stable-unstable manifolds associated with those nonlinear evolution equations. In the second half of the book, he shows how to apply the abstract results to various models in the real world focusing on various self-organization models: semiconductor model, activator-inhibitor model, B-Z reaction model, forest kinematic model, chemotaxis model, termite mound building model, phase transition model, and Lotka-Volterra competition model. The process and techniques are explained concretely in order to analyze nonlinear diffusion models by using the methods of abstract evolution equations. Thus the present book fills the gaps of related titles that either treat only very theoretical examples of equations or introduce many interesting models from Biology and Ecology, but do not base analytical arguments upon rigorous mathematical theories.
| Author | : Jerome A. Goldstein |
| Publisher | : Routledge |
| Total Pages | : 353 |
| Release | : 2017-10-05 |
| Genre | : Mathematics |
| ISBN | : 1351455184 |
Download Differential Equations with Applications in Biology, Physics, and Engineering Book in PDF, ePub and Kindle
Suitable as a textbook for a graduate seminar in mathematical modelling, and as a resource for scientists in a wide range of disciplines. Presents 22 lectures from an international conference in Leibnitz, Austria (no date mentioned), explaining recent developments and results in differential equatio
| Author | : Marius Ghergu |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 402 |
| Release | : 2011-10-21 |
| Genre | : Mathematics |
| ISBN | : 3642226647 |
Download Nonlinear PDEs Book in PDF, ePub and Kindle
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 | : Ionuţ Munteanu |
| Publisher | : Springer |
| Total Pages | : 214 |
| Release | : 2019-02-15 |
| Genre | : Science |
| ISBN | : 3030110990 |
Download Boundary Stabilization of Parabolic Equations Book in PDF, ePub and Kindle
This monograph presents a technique, developed by the author, to design asymptotically exponentially stabilizing finite-dimensional boundary proportional-type feedback controllers for nonlinear parabolic-type equations. The potential control applications of this technique are wide ranging in many research areas, such as Newtonian fluid flows modeled by the Navier-Stokes equations; electrically conducted fluid flows; phase separation modeled by the Cahn-Hilliard equations; and deterministic or stochastic semi-linear heat equations arising in biology, chemistry, and population dynamics modeling. The text provides answers to the following problems, which are of great practical importance: Designing the feedback law using a minimal set of eigenfunctions of the linear operator obtained from the linearized equation around the target state Designing observers for the considered control systems Constructing time-discrete controllers requiring only partial knowledge of the state After reviewing standard notations and results in functional analysis, linear algebra, probability theory and PDEs, the author describes his novel stabilization algorithm. He then demonstrates how this abstract model can be applied to stabilization problems involving magnetohydrodynamic equations, stochastic PDEs, nonsteady-states, and more. Boundary Stabilization of Parabolic Equations will be of particular interest to researchers in control theory and engineers whose work involves systems control. Familiarity with linear algebra, operator theory, functional analysis, partial differential equations, and stochastic partial differential equations is required.
| Author | : King-Yeung Lam |
| Publisher | : Springer Nature |
| Total Pages | : 316 |
| Release | : 2022-12-01 |
| Genre | : Mathematics |
| ISBN | : 3031204220 |
Download Introduction to Reaction-Diffusion Equations Book in PDF, ePub and Kindle
This book introduces some basic mathematical tools in reaction-diffusion models, with applications to spatial ecology and evolutionary biology. It is divided into four parts. The first part is an introduction to the maximum principle, the theory of principal eigenvalues for elliptic and periodic-parabolic equations and systems, and the theory of principal Floquet bundles. The second part concerns the applications in spatial ecology. We discuss the dynamics of a single species and two competing species, as well as some recent progress on N competing species in bounded domains. Some related results on stream populations and phytoplankton populations are also included. We also discuss the spreading properties of a single species in an unbounded spatial domain, as modeled by the Fisher-KPP equation. The third part concerns the applications in evolutionary biology. We describe the basic notions of adaptive dynamics, such as evolutionarily stable strategies and evolutionary branching points, in the context of a competition model of stream populations. We also discuss a class of selection-mutation models describing a population structured along a continuous phenotypical trait. The fourth part consists of several appendices, which present a self-contained treatment of some basic abstract theories in functional analysis and dynamical systems. Topics include the Krein-Rutman theorem for linear and nonlinear operators, as well as some elements of monotone dynamical systems and abstract competition systems. Most of the book is self-contained and it is aimed at graduate students and researchers who are interested in the theory and applications of reaction-diffusion equations.
