Singularities of Solutions to Chemotaxis Systems
Singularities of Solutions to Chemotaxis Systems

Author: Piotr Biler

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2019-12-02

Total Pages: 177

ISBN-13: 3110598620

DOWNLOAD EBOOK

The Keller-Segel model for chemotaxis is a prototype of nonlocal systems describing concentration phenomena in physics and biology. While the two-dimensional theory is by now quite complete, the questions of global-in-time solvability and blowup characterization are largely open in higher dimensions. In this book, global-in-time solutions are constructed under (nearly) optimal assumptions on initial data and rigorous blowup criteria are derived.

Singularities of Solutions to Chemotaxis Systems
Singularities of Solutions to Chemotaxis Systems

Author: Piotr Biler

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2019-12-02

Total Pages: 232

ISBN-13: 3110599538

DOWNLOAD EBOOK

The Keller-Segel model for chemotaxis is a prototype of nonlocal systems describing concentration phenomena in physics and biology. While the two-dimensional theory is by now quite complete, the questions of global-in-time solvability and blowup characterization are largely open in higher dimensions. In this book, global-in-time solutions are constructed under (nearly) optimal assumptions on initial data and rigorous blowup criteria are derived.

One-Locus and Multi-Locus Theory and Recombination
One-Locus and Multi-Locus Theory and Recombination

Author: Igor M. Rouzine

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2020-11-23

Total Pages: 207

ISBN-13: 3110608197

DOWNLOAD EBOOK

The book will benefit a reader with a background in physical sciences and applied mathematics interested in the mathematical models of genetic evolution. In the first chapter, we analyze several thought experiments based on a basic model of stochastic evolution of a single genomic site in the presence of the factors of random mutation, directional natural selection, and random genetic drift. In the second chapter, we present a more advanced theory for a large number of linked loci. In the third chapter, we include the effect of genetic recombination into account and find out the advantage of sexual reproduction for adaptation. These models are useful for the evolution of a broad range of asexual and sexual populations, including virus evolution in a host and a host population.

Mean Field Theories and Dual Variation - Mathematical Structures of the Mesoscopic Model
Mean Field Theories and Dual Variation - Mathematical Structures of the Mesoscopic Model

Author: Takashi Suzuki

Publisher: Springer

Published: 2015-11-19

Total Pages: 450

ISBN-13: 9462391548

DOWNLOAD EBOOK

Mean field approximation has been adopted to describe macroscopic phenomena from microscopic overviews. It is still in progress; fluid mechanics, gauge theory, plasma physics, quantum chemistry, mathematical oncology, non-equilibirum thermodynamics. spite of such a wide range of scientific areas that are concerned with the mean field theory, a unified study of its mathematical structure has not been discussed explicitly in the open literature. The benefit of this point of view on nonlinear problems should have significant impact on future research, as will be seen from the underlying features of self-assembly or bottom-up self-organization which is to be illustrated in a unified way. The aim of this book is to formulate the variational and hierarchical aspects of the equations that arise in the mean field theory from macroscopic profiles to microscopic principles, from dynamics to equilibrium, and from biological models to models that arise from chemistry and physics.

Analysis of Reaction-Diffusion Models with the Taxis Mechanism
Analysis of Reaction-Diffusion Models with the Taxis Mechanism

Author: Yuanyuan Ke

Publisher: Springer Nature

Published: 2022-08-25

Total Pages: 418

ISBN-13: 981193763X

DOWNLOAD EBOOK

This open access book deals with a rich variety of taxis-type cross-diffusive equations. Particularly, it intends to show the key role played by quasi-energy inequality in the derivation of some necessary a priori estimates. This book addresses applied mathematics and all researchers interested in mathematical development of reaction-diffusion theory and its application and can be a basis for a graduate course in applied mathematics.

Singularities in PDE and the Calculus of Variations
Singularities in PDE and the Calculus of Variations

Author: Stanley Alama

Publisher: American Mathematical Soc.

Published:

Total Pages: 284

ISBN-13: 9780821873311

DOWNLOAD EBOOK

This book contains papers presented at the "Workshop on Singularities in PDE and the Calculus of Variations" at the CRM in July 2006. The main theme of the meeting was the formation of geometrical singularities in PDE problems with a variational formulation. These equations typically arise in some applications (to physics, engineering, or biology, for example) and their resolution often requires a combination of methods coming from areas such as functional and harmonic analysis, differential geometry and geometric measure theory. Among the PDE problems discussed were: the Cahn-Hilliard model of phase transitions and domain walls; vortices in Ginzburg-Landau type models for superconductivity and superfluidity; the Ohna-Kawasaki model for di-block copolymers; models of image enhancement; and Monge-Ampere functions. The articles give a sampling of problems and methods in this diverse area of mathematics, which touches a large part of modern mathematics and its applications.

Free Energy and Self-Interacting Particles
Free Energy and Self-Interacting Particles

Author: Takashi Suzuki

Publisher: Springer Science & Business Media

Published: 2008-01-08

Total Pages: 367

ISBN-13: 0817644369

DOWNLOAD EBOOK

* Examines a nonlinear system of parabolic PDEs arising in mathematical biology and statistical mechanics * Describes the whole picture, i.e., the mathematical and physical principles * Suitable for researchers and grad students in mathematics and applied mathematics who are interested in nonlinear PDEs in stochastic processes, cellular automatons, variational methods, and their applications to physics, chemistry, biology, and engineering

Asymptotic Analysis and Singularities: Elliptic and parabolic PDEs and related problems
Asymptotic Analysis and Singularities: Elliptic and parabolic PDEs and related problems

Author: Hideo Kozono

Publisher:

Published: 2007

Total Pages: 432

ISBN-13: 9784931469419

DOWNLOAD EBOOK

This volume is the proceedings of the 14th MSJ International Research Institute "Asymptotic Analysis and Singularity", which was held at Sendai, Japan in July 2005. The proceedings contain survey papers and original research papers on nonlinear partial differential equations, dynamical systems, calculus of variations and mathematical physics.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets except North America