The effects of diffusion and spatial variation in lotkavolterra. Society for industrial and applied mathematics siam, philadelphia, pa, 2011. Weiming ni and izumi takagi, on the existence and shape of solutions to a semilinear neumann problem, nonlinear diffusion equations and their equilibrium states, 3, 10. An elliptic approach yuan lou department of mathematics, university of chicago, chicago, illinois 60637 and weiming ni school of mathematics, university of minnesota, minneapolis, minnesota 55455 received march 3, 1998. For the case of more mathematical interest, the singular limit. Pdf the mathematics of diffusion download full pdf. The carrying capacity of the environment for a population is one of the key concepts in ecology and it is incorporated in the growth term of reaction diffusion equations describing populations in space. Wei ming ni s 65 research works with 3,690 citations and 4,960 reads, including. Introduction in this paper we study positive steadystate solutions to the following stronglycoupled parabolic system. The mathematics of diffusion focuses on the qualitative properties of solutions to nonlinear elliptic and parabolic equations and systems in connection with domain geometry, various boundary conditions, the mechanism of different diffusion rates, and the interaction between diffusion and spatial heterogeneity.
The mathematics of diffusion focuses on the qualitative properties of solutions to nonlinear elliptic and parabolic equations and systems in. In this paper, we discuss limiting systems of the model as the cross diffusion rates included in the nonlinear diffusion tend to infinity. An introduction to variational inequalities and their applications david kinderlehrer, guido stampacchia subject. Diffusion has been used extensively in many scientific disciplines to model a wide variety of phenomena. Author links open overlay panel yuan lou weiming ni. Degenerate diffusions the ima volumes in mathematics and its.
To further illustrate the general results obtained in part i he and ni in commun pure appl math 69. Weiming nis 65 research works with 3,690 citations and 4,960 reads, including. Mathematical aspects of patternformation in biological systems will be of interest to graduate students and researchers who are active in reactiondiffusion systems, pattern formation and. For heterogeneous environments we study the existence and stability of positive steady states. Hypothesis for origin of planktonic patchiness nature. The carrying capacity of the environment for a population is one of the key concepts in ecology and it is incorporated in the growth term of reactiondiffusion equations describing populations in space. The mathematics of diffusion focuses on the qualitative properties of solutions to nonlinear elliptic and parabolic equations and systems in connection with domain geometry, various boundary conditions, the mechanism of different diffusion rates, and the interaction between diffusion and. It deals with the description of diffusion processes in terms of solutions of the differential equation for diffusion. Diffusion, selfdiffusion and crossdiffusion sciencedirect. Author links open overlay panel yuan lou wei ming ni. Usually one thinks of diffusion as damping inhomogeneities, and a hypothesis put forward by steele 2 essentially relies on a balance reached between. Weiming ni holds a joint appointment as the director of the center for partial. Other readers will always be interested in your opinion of the books youve read. According to our current online database, wei ming ni has 17 students and 70 descendants.
Effect of stressors on the carrying capacity of spatially distributed metapopulations. Download an introduction to variational inequalities and. Cbmsnsf regional conference series in applied mathematics the mathematics of diffusion. We study the dynamics of a consumerresource reactiondiffusion model, in both homogeneous and heterogeneous environments. The mathematics of diffusion by weiming ni 2011 english pdf. Cbmsnsf regional conference series in applied mathematics, 82. In this paper, we discuss limiting systems of the model as the crossdiffusion rates included in the nonlinear diffusion tend to infinity. Mathematical aspects of patternformation in biological systems will be of interest to graduate students and researchers who are active in reaction diffusion systems, pattern formation and mathematical biology. Nonlinear functional analysis, partial differential equations. University of sao paulo institute of mathematics and computer science, sao. The mathematics of diffusion cbmsnsf regional conference. Gidas, ni, nirenberg project euclid mathematics and. Reaction diffusion system approximations to a cross diffusion system are investigated.
Last but not least, andrew odlyzko is also ending his time 6 years as director of the digital technology center and will be returning to the school of mathematics, after spending some highly deserved time on leave next year. For heterogeneous environments we study the existence and stability of positive steady states and the. Analysis of reaction diffusion models of populations in heterogeneous space have shown that, when the maximum growth rate and carrying capacity in a logistic growth function vary in space. Department of mathematics, university of chicago, 5734. Usually one thinks of diffusion as damping inhomogeneities, and a hypothesis put forward by steele 2 essentially relies on a balance reached between the dehomogenising aspects of local interaction. Pdf on the global existence of a crossdiffusion system. The articles published are addressed not only to mathematicians but also to those engineers, physicists, and other scientists for whom differential equations are valuable research tools. Download fulltext pdf download fulltext pdf download fulltext pdf download fulltext pdf download fulltext pdf. Whether youve loved the book or not, if you give your honest and detailed thoughts then people will find new books that are right for them. Aug 23, 2017 in this paperpart iii of this series of three papers, we continue to investigate the joint effects of diffusion and spatial concentration on the global dynamics of the classical lotkavolterra competitiondiffusion system. Global dynamics of the lotkavolterra competitiondiffusion. Refuting previous theory, however, we discovered that homogeneously distributed resources support. In this paperpart iii of this series of three papers, we continue to investigate the joint effects of diffusion and spatial concentration on the global dynamics of the classical lotkavolterra competitiondiffusion system.
We study the existence, uniqueness and stability of positive steady states and the persistence of timedependent solutions. Format plenary invited lectures 50minute, special sessions 30minute talkdiscussion, contributed sessions 20minute talkdiscussion, and poster session and student paper competition. Citescore values are based on citation counts in a given year e. The real symmetric case cipolloni, giorgio, erdos, laszlo, kruger, torben, and schroder, dominik, pure and applied analysis, 2019. Ni, weiming global dynamics of the lotka volterra competitiondiffusion system with equal amount of total resources, iii. Jun 12, 2018 we study the dynamics of a consumerresource reaction diffusion model, in both homogeneous and heterogeneous environments. In this chapter we discuss some reactiondiffusion models for single and. Saddle solutions of the bistable diffusion equation springerlink. Diffusion, selfdiffusion and crossdiffusion yuan lou and weiming ni school of mathematics, university of minnesota, minneapolis, minnesota 55455 received december, 1995 1. An intriguing recent result from mathematics is that a population diffusing at an intermediate rate in an environment in which resources vary spatially will reach a higher total equilibrium biomass than the population in an environment in which the same total resources are distributed homogeneously. Journal finder download the understanding the publishing process pdf. Nirenberg,symmetry and related properties via the maximum principle, commun. On the limiting system in the shigesada, kawasaki and.
Kanstability of singularly perturbed solutions to nonlinear diffusion system arising in population dynamics. The mathematics of diffusion focuses on the qualitative properties of solutions to. Ohio, united states email yuan lou elliptic, reactiondiffusion equations. Download pdf the mathematics of diffusion book full free.
Diffusion, crossdiffusion, and their spikelayer steady states. If you would like to contribute, please donate online using credit card or bank transfer or mail your taxdeductible contribution to. Pdf the mathematics of diffusion download full pdf book. Ni, weiming global dynamics of the lotkavolterra competitiondiffusion system with equal amount of total resources, iii. Iida and ninomiyarecent advances on elliptic and parabolic issues, 145164 2006 proposed a semilinear reactiondiffusion system with a small parameter and showed that the limit equation takes the form of a weakly coupled crossdiffusion system provided that solutions of both the reactiondiffusion and. We study the dynamics of a consumerresource reactiondiffusion model, proposed recently by zhang et al. During the program, xuefeng wang tulane university taught a crash course in pdes, and weiming ni university of minnesota delivered a series of lectures on reactiondiffusion systems.
Download an introduction to variational inequalities and their applications, david kinderlehrer, guido stampacchia, academic press, 1980 author. The mathematics genealogy project is in need of funds to help pay for student help and other associated costs. The effects of diffusion and spatial variation in the lotka. Analysis of reactiondiffusion models of populations in heterogeneous space have shown that, when the maximum growth rate and carrying capacity in a logistic growth function vary in space. Carrying capacity of a population diffusing in a heterogeneous.
A comparison of homogeneous vs heterogeneous environments will be included. First week second week third week may 18 friday, pm 2. Weiming nis research works the chinese university of hong. To submit students of this mathematician, please use the new data form, noting this mathematicians mgp id of 11637 for the advisor id. Yuan lous research works the ohio state university, oh osu. The journal of differential equations is concerned with the theory and the application of differential equations. Reactiondiffusion system approximations to a crossdiffusion system are investigated. On the global existence of a crossdiffusion system. A complete description of the entire dynamics of the kinetic system, i. The theme of the applied math program was the effect of diffusion on the solutions of reactiondiffusion equations. Iida and ninomiyarecent advances on elliptic and parabolic issues, 145164 2006 proposed a semilinear reaction diffusion system with a small parameter and showed that the limit equation takes the form of a weakly coupled cross diffusion system provided that solutions of both the reaction diffusion and. In this thesis, using the classical lotkavolterra competition system, we will illustrate the combined effects of dispersal and spatial variation on the outcome of the competition.
Weiming ni, ecnu, china, and university of minnesota, usa diffusion and spatial heterogeneity chiunchuan chen, national taiwan university, taiwan to be announced. For homogeneous environments we establish the global stability of constant steady states. Mathematical aspects of pattern formation in biological. Introduction in this paper, we continue our study initiated in 4 on. We consider a reactiondiffusion system consisting of an activator and an inhibitor which models biological pattern formation. The chinese university of hong kong, hong kong, hong kong email weiming ni. If you have additional information or corrections regarding this mathematician, please use the update form. Consistent with previous theory, we predicted and experimentally observed that spatial diffusion increased total equilibrium population abundance in heterogeneous environments, with the effect size depending on the relationship between r and k. Back matter the mathematics of diffusion society for. The mathematics of diffusion available for download and read online in other formats. Deangelis 1, bo zhang 2, weiming ni 3,4 and yuanshi wang 5. Geological survey, wetland and aquatic research center, gainesville, florida.
Yuanhua deng, goong chen, weiming ni and jianxin zhou. According to our current online database, weiming ni has 17 students and 70 descendants. Sample chapters fixed points of twist mappings and periodic solutions of ordinary differential equations. Little mention is made of the alternative, but less well developed. Wei ming ni and izumi takagi, on the existence and shape of solutions to a semilinear neumann problem, nonlinear diffusion equations and their equilibrium states, 3, 10.
Buy degenerate diffusions the ima volumes in mathematics and its applications on free shipping on qualified orders. Xiaoqing he and weiming ni, the effects of diffusion and spatial variation in lotkavolterra competitiondiffusion system ii. A competing species problem is studied in the limiting cases of small and large diffusion the question of permanence is resolved. Stationary solutions of the bistable cahnallen diffusion equation in the plane are.
On a final note, this is the last time i am writing as. The articles published are addressed not only to mathematicians but also to those engineers, physicists, and other scientists for whom differential equations. Prof weiyue ding devoted his academic career to the research in the field of ordinary differential equations and geometric analysis, e. We consider a reaction diffusion system consisting of an activator and an inhibitor which models biological pattern formation. Dynamics of a consumerresource reactiondiffusion model. Jul 09, 2018 format plenary invited lectures 50minute, special sessions 30minute talkdiscussion, contributed sessions 20minute talkdiscussion, and poster session and student paper competition. The aim of this workshop was to provide some focus in the study of degenerate diffusion equations, and by involving scientists and engineers as well as mathematicians, to keep this focus firmly linked to concrete problems. It is well known that the interactions between diffusion and spatial heterogeneity could create very interesting phenomena. A relation between crossdiffusion and reactiondiffusion. School of mathematics, university of minnesota, minneapolis, minnesota 55455. Takagipoint condensation generated by a reactiondiffusion.
1113 215 651 66 659 1240 556 205 415 83 781 1224 1540 1116 183 88 780 1188 1121 789 1595 1315 1471 1112 1357 138 978 956 1175 904 34 1297 536