Analysis of Two Classes of Cross Diffusion Systems PDF Download
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Author: Hassan Jawad Al Salman
Publisher:
ISBN:
Category :
Languages : en
Pages : 204
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Book Description
Abstract: A mathematical and numerical analysis has been carried out for two cross diffusion systems arising in applied mathematics. The first system appears in modelling the movement of two interacting cell populations whose kinetics are of competition type. The second system models axial segregation of a mixture of two different granular materials in a long rotating drum. A fully practical piecewise linear finite element approximation for each system is proposed and studied. With the aid of a fixed point theorem, existence of the fully discrete solutions is shown. By using entropy-type inequalities and compactness arguments, the convergence of the approximation of each system is proved and hence existence of a global weak solution is obtained. Providing further regularity of the solution of the axial segregation model, some uniqueness results and error estimates are established. The long time behaviour of both systems is investigated and estimates between the weak solutions and the mean integrals of the corresponding initial data are derived. Finally, a practical algorithm for computing the numerical solutions of each system is described and some numerical experiments are performed to illustrate and verify the theoretical results.
Author: Hassan Jawad Al Salman
Publisher:
ISBN:
Category :
Languages : en
Pages : 204
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Book Description
Abstract: A mathematical and numerical analysis has been carried out for two cross diffusion systems arising in applied mathematics. The first system appears in modelling the movement of two interacting cell populations whose kinetics are of competition type. The second system models axial segregation of a mixture of two different granular materials in a long rotating drum. A fully practical piecewise linear finite element approximation for each system is proposed and studied. With the aid of a fixed point theorem, existence of the fully discrete solutions is shown. By using entropy-type inequalities and compactness arguments, the convergence of the approximation of each system is proved and hence existence of a global weak solution is obtained. Providing further regularity of the solution of the axial segregation model, some uniqueness results and error estimates are established. The long time behaviour of both systems is investigated and estimates between the weak solutions and the mean integrals of the corresponding initial data are derived. Finally, a practical algorithm for computing the numerical solutions of each system is described and some numerical experiments are performed to illustrate and verify the theoretical results.
Author: Huda Abduljabbar Challoob
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: Dung Le
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110795132
Category : Mathematics
Languages : en
Pages : 236
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Book Description
The introduction of cross diffusivity opens many questions in the theory of reactiondiffusion systems. This book will be the first to investigate such problems presenting new findings for researchers interested in studying parabolic and elliptic systems where classical methods are not applicable. In addition, The Gagliardo-Nirenberg inequality involving BMO norms is improved and new techniques are covered that will be of interest. This book also provides many open problems suitable for interested Ph.D students.
Author:
Publisher: ScholarlyEditions
ISBN: 1490109544
Category : Mathematics
Languages : en
Pages : 1182
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Book Description
Issues in General and Specialized Mathematics Research: 2013 Edition is a ScholarlyEditions™ book that delivers timely, authoritative, and comprehensive information about General Mathematics. The editors have built Issues in General and Specialized Mathematics Research: 2013 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about General Mathematics in this book to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in General and Specialized Mathematics Research: 2013 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.
Author: Pierre-Étienne Druet
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
We investigate degenerate cross-diffusion equations with a rank-deficient diffusion matrix that are considered to model populations which move as to avoid spatial crowding and have recently been found to arise in a mean-field limit of interacting stochastic particle systems. To date, their analysis in multiple space dimensions has been confined to the purely convective case with equal mobility coefficients. In this article, we introduce a normal form for an entropic class of suchequations which reveals their structure of a symmetric hyperbolic-parabolic system. Due to the state-dependence of the range and kernel of the singular diffusive matrix, our way of rewriting the equations is different from that classically used for symmetric second-order systems with a nullspace invariance property. By means of this change of variables, we solve the Cauchy problem for short times and positive initial data in Hs(Td) for s > d=2 + 1.
Author: Roger Temam
Publisher: Springer Science & Business Media
ISBN: 1461206456
Category : Mathematics
Languages : en
Pages : 670
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Book Description
In this book the author presents the dynamical systems in infinite dimension, especially those generated by dissipative partial differential equations. This book attempts a systematic study of infinite dimensional dynamical systems generated by dissipative evolution partial differential equations arising in mechanics and physics and in other areas of sciences and technology. This second edition has been updated and extended.
Author: Tatsien Li
Publisher: World Scientific
ISBN: 9814547840
Category :
Languages : en
Pages : 242
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Book Description
The aim of the symposium was to provide a forum for presenting and discussing recent developments and trends in Reaction-diffusion Equations and to promote scientific exchanges among mathematicians in China and in Japan, especially for the younger generation. The topics discussed were: Layer dynamics, Traveling wave solutions and its stability, Equilibrium solutions and its limit behavior (stability), Bifurcation phenomena, Computational solutions, and Infinite dimensional dynamical system.
Author:
Publisher:
ISBN:
Category : Nuclear energy
Languages : en
Pages : 964
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Book Description
Author:
Publisher:
ISBN:
Category : Mechanics, Applied
Languages : en
Pages : 616
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Author: Pierre-Étienne Druet
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
The convective transport in a multicomponent isothermal compressible fluid subject to the mass continuity equations is considered. The velocity is proportional to the negative pressure gradient, according to Darcy’s law, and the pressure is defined by a state equation imposed by the volume extension of the mixture. These model assumptions lead to a parabolic-hyperbolic system for the mass densities. The global-in-time existence of classical and weak solutions is proved in a bounded domain with no-penetration boundary conditions. The idea is to decompose the system into a porous-medium-type equation for the volume extension and transport equations for the modified number fractions. The existence proof is based on parabolic regularity theory, the theory of renormalized solutions, and an approximation of the velocity field.
