Free Boundary Problems in PDEs and Particle Systems PDF Download
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Author: Gioia Carinci
Publisher: Springer
ISBN: 3319333704
Category : Mathematics
Languages : en
Pages : 106
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Book Description
In this volume a theory for models of transport in the presence of a free boundary is developed.Macroscopic laws of transport are described by PDE's. When the system is open, there are several mechanisms to couple the system with the external forces. Here a class of systems where the interaction with the exterior takes place in correspondence of a free boundary is considered. Both continuous and discrete models sharing the same structure are analysed. In Part I a free boundary problem related to the Stefan Problem is worked out in all details. For this model a new notion of relaxed solution is proposed for which global existence and uniqueness is proven. It is also shown that this is the hydrodynamic limit of the empirical mass density of the associated particle system. In Part II several other models are discussed. The expectation is that the results proved for the basic model extend to these other cases.All the models discussed in this volume have an interest in problems arising in several research fields such as heat conduction, queuing theory, propagation of fire, interface dynamics, population dynamics, evolution of biological systems with selection mechanisms.In general researchers interested in the relations between PDE’s and stochastic processes can find in this volume an extension of this correspondence to modern mathematical physics.
Author: Gioia Carinci
Publisher: Springer
ISBN: 3319333704
Category : Mathematics
Languages : en
Pages : 106
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Book Description
In this volume a theory for models of transport in the presence of a free boundary is developed.Macroscopic laws of transport are described by PDE's. When the system is open, there are several mechanisms to couple the system with the external forces. Here a class of systems where the interaction with the exterior takes place in correspondence of a free boundary is considered. Both continuous and discrete models sharing the same structure are analysed. In Part I a free boundary problem related to the Stefan Problem is worked out in all details. For this model a new notion of relaxed solution is proposed for which global existence and uniqueness is proven. It is also shown that this is the hydrodynamic limit of the empirical mass density of the associated particle system. In Part II several other models are discussed. The expectation is that the results proved for the basic model extend to these other cases.All the models discussed in this volume have an interest in problems arising in several research fields such as heat conduction, queuing theory, propagation of fire, interface dynamics, population dynamics, evolution of biological systems with selection mechanisms.In general researchers interested in the relations between PDE’s and stochastic processes can find in this volume an extension of this correspondence to modern mathematical physics.
Author: S.N. Antontsev
Publisher: Springer Science & Business Media
ISBN: 1461200911
Category : Technology & Engineering
Languages : en
Pages : 338
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Book Description
For the past several decades, the study of free boundary problems has been a very active subject of research occurring in a variety of applied sciences. What these problems have in common is their formulation in terms of suitably posed initial and boundary value problems for nonlinear partial differential equations. Such problems arise, for example, in the mathematical treatment of the processes of heat conduction, filtration through porous media, flows of non-Newtonian fluids, boundary layers, chemical reactions, semiconductors, and so on. The growing interest in these problems is reflected by the series of meetings held under the title "Free Boundary Problems: Theory and Applications" (Ox ford 1974, Pavia 1979, Durham 1978, Montecatini 1981, Maubuisson 1984, Irsee 1987, Montreal 1990, Toledo 1993, Zakopane 1995, Crete 1997, Chiba 1999). From the proceedings of these meetings, we can learn about the different kinds of mathematical areas that fall within the scope of free boundary problems. It is worth mentioning that the European Science Foundation supported a vast research project on free boundary problems from 1993 until 1999. The recent creation of the specialized journal Interfaces and Free Boundaries: Modeling, Analysis and Computation gives us an idea of the vitality of the subject and its present state of development. This book is a result of collaboration among the authors over the last 15 years.
Author: Cédric Bernardin
Publisher: Springer
ISBN: 9783030697860
Category : Mathematics
Languages : en
Pages : 400
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Book Description
This book includes the joint proceedings of the International Conference on Particle Systems and PDEs VI, VII and VIII. Particle Systems and PDEs VI was held in Nice, France, in November/December 2017, Particle Systems and PDEs VII was held in Palermo, Italy, in November 2018, and Particle Systems and PDEs VIII was held in Lisbon, Portugal, in December 2019. Most of the papers are dealing with mathematical problems motivated by different applications in physics, engineering, economics, chemistry and biology. They illustrate methods and topics in the study of particle systems and PDEs and their relation. The book is recommended to probabilists, analysts and to those mathematicians in general, whose work focuses on topics in mathematical physics, stochastic processes and differential equations, as well as to those physicists who work in statistical mechanics and kinetic theory.
Author:
Publisher:
ISBN:
Category : Aeronautics
Languages : en
Pages : 1460
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Book Description
Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.
Author: Mark A. Pinsky
Publisher: American Mathematical Soc.
ISBN: 0821868896
Category : Mathematics
Languages : en
Pages : 545
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Book Description
Building on the basic techniques of separation of variables and Fourier series, the book presents the solution of boundary-value problems for basic partial differential equations: the heat equation, wave equation, and Laplace equation, considered in various standard coordinate systems--rectangular, cylindrical, and spherical. Each of the equations is derived in the three-dimensional context; the solutions are organized according to the geometry of the coordinate system, which makes the mathematics especially transparent. Bessel and Legendre functions are studied and used whenever appropriate throughout the text. The notions of steady-state solution of closely related stationary solutions are developed for the heat equation; applications to the study of heat flow in the earth are presented. The problem of the vibrating string is studied in detail both in the Fourier transform setting and from the viewpoint of the explicit representation (d'Alembert formula). Additional chapters include the numerical analysis of solutions and the method of Green's functions for solutions of partial differential equations. The exposition also includes asymptotic methods (Laplace transform and stationary phase). With more than 200 working examples and 700 exercises (more than 450 with answers), the book is suitable for an undergraduate course in partial differential equations.
Author: Pierluigi Colli
Publisher: Birkhäuser
ISBN: 3034878931
Category : Mathematics
Languages : en
Pages : 342
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Book Description
Many phenomena of interest for applications are represented by differential equations which are defined in a domain whose boundary is a priori unknown, and is accordingly named a "free boundary". A further quantitative condition is then provided in order to exclude indeterminacy. Free boundary problems thus encompass a broad spectrum which is represented in this state-of-the-art volume by a variety of contributions of researchers in mathematics and applied fields like physics, biology and material sciences. Special emphasis has been reserved for mathematical modelling and for the formulation of new problems.
Author: Marek Niezgodka
Publisher: CRC Press
ISBN: 9780582305939
Category : Mathematics
Languages : en
Pages : 462
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Book Description
Addressing various aspects of nonlinear partial differential equations, this volume contains papers and lectures presented at the Congress on Free boundary Problems, Theory and Application held in Zakopane, Poland in 1995. Topics include existence, uniqueness, asymptotic behavior, and regularity of solutions and interfaces.
Author: National Science Foundation (U.S.)
Publisher:
ISBN:
Category : Federal aid to research
Languages : en
Pages : 260
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Book Description
Author: Satoshi Nakata
Publisher: Royal Society of Chemistry
ISBN: 1788015436
Category : Science
Languages : en
Pages : 388
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Book Description
Self-propelled objects (particles, droplets) are autonomous agents that can convert energy from the environment into motion. These motions include nonlinear behaviour such as oscillations, synchronization, bifurcation, and pattern formation. In recent years, there has been much interest in self-propelled objects for their potential role in mass transport or their use as carriers in confined spaces. An improved understanding of self-organized motion has even allowed researchers to design objects for specific motion. This book gives an overview of the principles of self-propelled motion in chemical objects (particles, droplets) far from their thermodynamic equilibrium, at various spatial scales. Theoretical aspects, the characteristics of the motion and the design procedures of such systems are discussed from the viewpoint of nonlinear dynamics and examples of applications for these nonlinear systems are provided. This book is suitable for researchers and graduate students interested in physical and theoretical chemistry as well as soft matter.
Author: Z. Zapryanov
Publisher: Springer Science & Business Media
ISBN: 9401592551
Category : Technology & Engineering
Languages : en
Pages : 527
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Book Description
1. Objective and Scope Bubbles, drops and rigid particles occur everywhere in life, from valuable industrial operations like gas-liquid contracting, fluidized beds and extraction to such vital natural processes as fermentation, evaporation, and sedimentation. As we become increasingly aware of their fundamental role in industrial and biological systems, we are driven to know more about these fascinating particles. It is no surprise, therefore, that their practical and theoretical implications have aroused great interest among the scientific community and have inspired a growing number of studies and publications. Over the past ten years advances in the field of small Reynolds numbers flows and their technological and biological applications have given rise to several definitive monographs and textbooks in the area. In addition, the past three decades have witnessed enormous progress in describing quantitatively the behaviour of these particles. However, to the best of our knowledge, there are still no available books that reflect such achievements in the areas of bubble and drop deformation, hydrodynamic interactions of deformable fluid particles at low and moderate Reynolds numbers and hydrodynamic interactions of particles in oscillatory flows. Indeed, only one more book is dedicated entirely to the behaviour of bubbles, drops and rigid particles ["Bubbles, Drops and Particles" by Clift et al. (1978)] and the authors state its limitations clearly in the preface: "We treat only phenomena in which particle-particle interactions are of negligible importance. Hence, direct application of the book is limited to single-particle systems of dilute suspensions.
