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Convergence Of Front Propagation For Anisotropic Bistable Reaction Diffusion Equations
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Book Synopsis Convergence of Front Propagation for Anisotropic Bistable Reaction-diffusion Equations by : Giovanni Bellettini
Download or read book Convergence of Front Propagation for Anisotropic Bistable Reaction-diffusion Equations written by Giovanni Bellettini and published by . This book was released on 1996 with total page 35 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Modeling of Physiological Flows by : Davide Ambrosi
Download or read book Modeling of Physiological Flows written by Davide Ambrosi and published by Springer Science & Business Media. This book was released on 2012-10-31 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a mathematical update of the state of the art of the research in the field of mathematical and numerical models of the circulatory system. It is structured into different chapters, written by outstanding experts in the field. Many fundamental issues are considered, such as: the mathematical representation of vascular geometries extracted from medical images, modelling blood rheology and the complex multilayer structure of the vascular tissue, and its possible pathologies, the mechanical and chemical interaction between blood and vascular walls, and the different scales coupling local and systemic dynamics. All of these topics introduce challenging mathematical and numerical problems, demanding for advanced analysis and efficient simulation techniques, and pay constant attention to applications of relevant clinical interest. This book is addressed to graduate students and researchers in the field of bioengineering, applied mathematics and medicine, wishing to engage themselves in the fascinating task of modeling the cardiovascular system or, more broadly, physiological flows.
Book Synopsis Calculus of Variations and Partial Differential Equations by : Luigi Ambrosio
Download or read book Calculus of Variations and Partial Differential Equations written by Luigi Ambrosio and published by Springer Science & Business Media. This book was released on 2000-01-24 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: At the summer school in Pisa in September 1996, Luigi Ambrosio and Norman Dancer each gave a course on the geometric problem of evolution of a surface by mean curvature, and degree theory with applications to PDEs respectively. This self-contained presentation accessible to PhD students bridged the gap between standard courses and advanced research on these topics. The resulting book is divided accordingly into 2 parts, and neatly illustrates the 2-way interaction of problems and methods. Each of the courses is augmented and complemented by additional short chapters by other authors describing current research problems and results.
Book Synopsis Complex Systems in Biomedicine by : A. Quarteroni
Download or read book Complex Systems in Biomedicine written by A. Quarteroni and published by Springer Science & Business Media. This book was released on 2007-03-20 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematicalmodelingofhumanphysiopathologyisatremendouslyambitioustask. It encompasses the modeling of most diverse compartments such as the cardiovas- lar,respiratory,skeletalandnervoussystems,aswellasthemechanicalandbioch- ical interaction between blood ?ow and arterial walls, and electrocardiac processes and electric conduction in biological tissues. Mathematical models can be set up to simulate both vasculogenesis (the aggregation and organization of endothelial cells dispersed in a given environment) and angiogenesis (the formation of new vessels sprouting from an existing vessel) that are relevant to the formation of vascular networks, and in particular to the description of tumor growth. The integration of models aimed at simulating the cooperation and interrelation of different systems is an even more dif?cult task. It calls for the setting up of, for instance, interaction models for the integrated cardio-vascular system and the interplay between the central circulation and peripheral compartments, models for the mid-to-long range cardiovascular adjustments to pathological conditions (e.g., to account for surgical interventions, congenital malformations, or tumor growth), models for integration among circulation, tissue perfusion, biochemical and thermal regulation, models for parameter identi?cation and sensitivity analysis to parameter changes or data uncertainty – and many others.
Book Synopsis Non-overlapping Domain Decomposition Methods for Three-dimensional Cardiac Reaction-diffusion Models and Applications by : Stefano Zampini
Download or read book Non-overlapping Domain Decomposition Methods for Three-dimensional Cardiac Reaction-diffusion Models and Applications written by Stefano Zampini and published by Ledizioni. This book was released on 2011 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent advances in biotechnology and the availability of ever more powerful computers have led to the formulation of increasingly complex models at all levels of life sciences, in particular of cardiac electrophysiology. Multiscale modeling of the bioelectric activity of the heart, taking into account macroscopic (fiber architecture and anisotropy) and microscopic (cellular) features of the tissue, aim to develop predictive tools for future drug design and patient-specific therapies, using detailed and efficient three-dimensional solvers for the governing equations of tissue electrophysiology.
Book Synopsis Two Examples of Reaction-diffusion Front Propagation in Heterogeneous Media by : Antoine Pauthier
Download or read book Two Examples of Reaction-diffusion Front Propagation in Heterogeneous Media written by Antoine Pauthier and published by . This book was released on 2016 with total page 131 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this thesis is to study two examples of propagation phenomena in heterogeneous reaction-diffusion equations.The purpose of the first part is to understand the effect of nonlocal exchanges between a line of fast diffusion and a two dimensional environment in which reaction-diffusion of KPP type occurs. The initial model was introduced in 2013 by Berestycki, Roquejoffre, and Rossi. In the first chapter we investigate how the nonlocal coupling between the line and the plane enhances the spreading in the direction of the line; we also investigate how different exchange functions may maximize or not the spreading speed.The second chapter is concerned with the singular limit of nonlocal exchanges that tend to Dirac masses. We show the convergence of the dynamics in a rather strong sense. In the third chapter we study the limit of long range exchanges with constant mass. It gives an infimum for the asymptotic speed of spreading for these models that still could be bigger than the usual KPP spreading speed.The second part of this thesis is concerned with entire solutions for heterogeneous bistable equations.We consider a two dimensional domain infinite in one direction, bounded in the other, that converges to a cylinder as x goes to minus infinity. We prove the existence of an entire solution in such a domain which is the bistable wave for t tends to minus infinity. It also lead us to investigate a one dimensional model with a non-homogeneous reaction term,for which we prove the same property.
Book Synopsis European Congress of Mathematics by : Carles Casacuberta
Download or read book European Congress of Mathematics written by Carles Casacuberta and published by Birkhäuser. This book was released on 2012-12-06 with total page 630 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second volume of the proceedings of the third European Congress of Mathematics. Volume I presents the speeches delivered at the Congress, the list of lectures, and short summaries of the achievements of the prize winners as well as papers by plenary and parallel speakers. The second volume collects articles by prize winners and speakers of the mini-symposia. This two-volume set thus gives an overview of the state of the art in many fields of mathematics and is therefore of interest to every professional mathematician.
Book Synopsis Front Propagation for Reaction-diffusion Equations of Bistable Type by : G. Barles
Download or read book Front Propagation for Reaction-diffusion Equations of Bistable Type written by G. Barles and published by . This book was released on 1990 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Electrocardiology '96: From The Cell To The Body Surface: Proceedings Of The Xxiii International Congress On Electroc by : J Liebman
Download or read book Electrocardiology '96: From The Cell To The Body Surface: Proceedings Of The Xxiii International Congress On Electroc written by J Liebman and published by World Scientific. This book was released on 1997-07-01 with total page 710 pages. Available in PDF, EPUB and Kindle. Book excerpt: This conference had as its focus the phrase 'From the Cell to the Body Surface'. It comprised five minisymposia, which concentrated on some of the major issues of the day for basic scientists and clinicians. In addition to the invited papers, the proceedings contain volume presentations and posters selected from among abstracts sent in by some of the most important investigators in electrocardiology worldwide.
Book Synopsis Proceedings of the International Congress of Mathematicians by : Marta Sanz Solé
Download or read book Proceedings of the International Congress of Mathematicians written by Marta Sanz Solé and published by . This book was released on 2006 with total page 854 pages. Available in PDF, EPUB and Kindle. Book excerpt: The International Congress of Mathematicians (ICM) is held every four years. It is a major scientific event, bringing together mathematicians from all over the world and demonstrating the vital role that mathematics play in our society. In particular, the Fields Medals are awarded to recognize outstanding mathematical achievement. At the same time, the International Mathematical Union awards the Nevanlinna Prize for work in the field of theoretical computer science. The proceedings of ICM 2006, published as a three-volume set, present an overview of current research in all areas of mathematics and provide a permanent record the congress. The first volume features the works of Fields Medallists and the Nevanlinna Prize winner, the plenary lectures, and the speeches and pictures of the opening and closing ceremonies and award sessions. The other two volumes present the invited lectures, arranged according to their mathematical subject.
Book Synopsis Mathematical Cardiac Electrophysiology by : Piero Colli Franzone
Download or read book Mathematical Cardiac Electrophysiology written by Piero Colli Franzone and published by Springer. This book was released on 2014-10-30 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers the main mathematical and numerical models in computational electrocardiology, ranging from microscopic membrane models of cardiac ionic channels to macroscopic bidomain, monodomain, eikonal models and cardiac source representations. These advanced multiscale and nonlinear models describe the cardiac bioelectrical activity from the cell level to the body surface and are employed in both the direct and inverse problems of electrocardiology. The book also covers advanced numerical techniques needed to efficiently carry out large-scale cardiac simulations, including time and space discretizations, decoupling and operator splitting techniques, parallel finite element solvers. These techniques are employed in 3D cardiac simulations illustrating the excitation mechanisms, the anisotropic effects on excitation and repolarization wavefronts, the morphology of electrograms in normal and pathological tissue and some reentry phenomena. The overall aim of the book is to present rigorously the mathematical and numerical foundations of computational electrocardiology, illustrating the current research developments in this fast-growing field lying at the intersection of mathematical physiology, bioengineering and computational biomedicine. This book is addressed to graduate student and researchers in the field of applied mathematics, scientific computing, bioengineering, electrophysiology and cardiology.
Book Synopsis Proceedings of International Conference On: Free Boundary Problems, Theory and Applications by : Nobuyuki Kenmochi
Download or read book Proceedings of International Conference On: Free Boundary Problems, Theory and Applications written by Nobuyuki Kenmochi and published by . This book was released on 2000 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Traveling Front Solutions in Reaction-Diffusion Equations by : Masaharu Taniguchi
Download or read book Traveling Front Solutions in Reaction-Diffusion Equations written by Masaharu Taniguchi and published by . This book was released on 2021-05-28 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study on traveling fronts in reaction-diffusion equations is the first step to understand various kinds of propagation phenomena in reaction-diffusion models in natural science. One dimensional traveling fronts have been studied from the 1970s, and multidimensional ones have been studied from around 2005. This volume is a text book for graduate students to start their studies on traveling fronts. Using the phase plane analysis, we study the existence of traveling fronts in several kinds of reaction-diffusion equations. For a nonlinear reaction term, a bistable one is a typical one. For a bistable reaction-diffusion equation, we study the existence and stability of two-dimensional V-form fronts, and we also study pyramidal traveling fronts in three or higher space dimensions. The cross section of a pyramidal traveling front forms a convex polygon. It is known that the limit of a pyramidal traveling front gives a new multidimensional traveling front. For the study the multidimensional traveling front, studying properties of pyramidal traveling fronts plays an important role. In this volume, we study the existence, uniqueness and stability of a pyramidal traveling front as clearly as possible for further studies by graduate students. For a help of their studies, we briefly explain and prove the well-posedness of reaction-diffusion equations and the Schauder estimates and the maximum principles of solutions.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets
Download or read book Mathematical Reviews written by and published by . This book was released on 2004 with total page 974 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Geometric Partial Differential Equations by : Antonin Chambolle
Download or read book Geometric Partial Differential Equations written by Antonin Chambolle and published by Springer Science & Business Media. This book was released on 2014-01-17 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the outcome of a conference held at the Centro De Giorgi of the Scuola Normale of Pisa in September 2012. The aim of the conference was to discuss recent results on nonlinear partial differential equations, and more specifically geometric evolutions and reaction-diffusion equations. Particular attention was paid to self-similar solutions, such as solitons and travelling waves, asymptotic behaviour, formation of singularities and qualitative properties of solutions. These problems arise in many models from Physics, Biology, Image Processing and Applied Mathematics in general, and have attracted a lot of attention in recent years.
Book Synopsis partial differential equations and applications by : Giorgio Talenti
Download or read book partial differential equations and applications written by Giorgio Talenti and published by Routledge. This book was released on 2017-10-02 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written as a tribute to the mathematician Carlo Pucci on the occasion of his 70th birthday, this is a collection of authoritative contributions from over 45 internationally acclaimed experts in the field of partial differential equations. Papers discuss a variety of topics such as problems where a partial differential equation is coupled with unfavourable boundary or initial conditions, and boundary value problems for partial differential equations of elliptic type.
Book Synopsis Advances in Mathematical Sciences and Applications by :
Download or read book Advances in Mathematical Sciences and Applications written by and published by . This book was released on 2000 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt:
