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Dissertations / Theses on the topic 'Reaction-diffusion waves'

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Published: 4 June 2021

Last updated: 3 February 2022

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1

Aldurayhim, Abdullah Mohammed. "Propagating waves in reaction cross-diffusion systems." Thesis, University of Exeter, 2017. http://hdl.handle.net/10871/31129.

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This research focuses on the reaction diffusion systems where the matrix of diffusion co- efficients is not diagonal. We call these systems reaction cross-diffusion systems. These systems possess interesting solutions that do not appear in the reaction self-diffusion systems that have a diagonal diffusion matrix. Compared to research conducted on re- action self-diffusion systems, the reaction cross-diffusion systems have received little attentions. The aim of this research is to extend existing literature on these systems. In this thesis we considered two-components reaction cross-diffusion s

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2

Fullwood, Timothy Brent. "Pattern formation and travelling waves in reaction-diffusion equations." Thesis, University of Warwick, 1995. http://wrap.warwick.ac.uk/4251/.

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This thesis is about pattern formation in reaction - diffusion equations, particularly Turing patterns and travelling waves. In chapter one we concentrate on Turing patterns. We give the classical approach to proving the existence of these patterns, and then our own, which uses the reversibility of the associated travelling wave equations when the wave speed is zero. We use a Lyapunov - Schmidt reduction to prove the existence of periodic solutions when there is a purely imaginary eigenvalue. We pay particular attention to the bifurcation point where these patterns arise, the 1: 1 resonance. W

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3

Hahn, Philip James. "Origination and Propagation of Reaction Diffusion Waves in Three Spatial Dimensions." Cleveland, Ohio : Case Western Reserve University, 2004. http://rave.ohiolink.edu/etdc/view?acc_num=case1091809306.

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Thesis(Ph.D.)--Case Western Reserve University, 2004<br>Title from PDF (viewed on 2009-11-23) Department of Mathematics Includes abstract Includes bibliographical references and appendices Available online via the OhioLINK ETD Center

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4

Carter, Mark. "Diffraction, interaction and core dynamics of reaction-diffusion waves : eikonal solutions." Thesis, Glasgow Caledonian University, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.267507.

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5

McDermott, Sean. "Reaction-diffusion waves on toroidal manifolds : eikonal and concomitant numerical solutions." Thesis, Glasgow Caledonian University, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.395793.

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6

Hahn, Philip James. "Origination and propagation of reaction diffusion waves in three spatial dimensions." online version, 2005. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=case1091809306.

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7

McCabe, Philip M. "The mathematical analysis of a class of singular reaction-diffusion systems." Thesis, University of Reading, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.301978.

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8

Franz, David, and University of Lethbridge Faculty of Arts and Science. "Turing patterns in linear chemical reaction systems with nonlinear cross diffusion." Thesis, Lethbridge, Alta. : University of Lethbridge, Faculty of Arts and Science, 2007, 2007. http://hdl.handle.net/10133/659.

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Turing patterns have been studied for over 50 years as a pattern forming mechanism. To date the current focus has been on the reaction mechanism, with little to no emphasis on the diffusion terms. This work focuses on combining the simplest reaction mechanism possible and the use of nonlinear cross diffusion to form Turing patterns. We start by using two methods of bifurcation analysis to show that our model can form a Turing instability. A diffusion model (along with some variants) is then presented along with the results of numerical simulations. Various tests on both the numerical methods a

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9

Haaf, Hermann. "Existence of periodic travelling waves to reaction-diffusion equations with excitable-oscillatory kinetics." Thesis, University of Warwick, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.387347.

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10

Ho, William Ka Wing. "Organisation of the feather periodic pattern through propagating molecular waves." Thesis, University of Edinburgh, 2016. http://hdl.handle.net/1842/25777.

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Members of the class Aves possess integumentary structures which distinguish them from other vertebrate lineages. The characteristic integumentary structure that defines the Aves from other vertebrates are the feathers, whose functions include insulation, camouflage, visual display, gliding, and powered flight. The recent discoveries of theropod dinosaur fossils displaying feather-like structures have led to interest in the morphological innovations of the feathers, which are associated with the evolution of flight in Aves. Most modern birds, display a highly ordered, hexagonal arrangement of

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11

Zhao, Huaizhong. "The stochastic elementary formula method and approximate travelling waves for semi-linear reaction diffusion equations." Thesis, University of Warwick, 1994. http://wrap.warwick.ac.uk/4236/.

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In this thesis we consider approximate travelling wave solutions for stochastic and generalised KPP equations and systems by using the stochastic elementary formula method of Elworthy and Truman. We begin with the semi-classical analysis for generalised KPP equations. With a so-called "late caustic" assumption we prove that the global wave front is given by the Hamilton Jacobi function. We prove a Huygens principle on complete Riemannian manifolds without cut locus, with some bounds on their volume elements, in particular Cartan-Hadamard manifolds. Based on the semiclassical analysis we then c

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12

Tsoi, Man. "Persistence of planar spiral waves under domain truncation near the core." Columbus, Ohio : Ohio State University, 2006. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1148486634.

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13

Dowdall, James. "Wave Blocking Phenomena and Ecological Applications." Thesis, Université d'Ottawa / University of Ottawa, 2015. http://hdl.handle.net/10393/33155.

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The growing flow of people and goods around the globe has allowed new, non-native species to establish and spread in already fragile ecosystems. The introduction of invasive species can have a detrimental impact on the already established species. Thus, it is important that we understand the mechanisms that facilitate or prevent invasion. Since reaction-diffusion invasion models produce travelling waves we can study invasion by looking at the mechanisms that allow for wave propagation failure, or wave-blocking. In this thesis we consider a perturbed reaction-diffusion model in which the pertur

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14

Spadotto, André Augusto. "Simulações de ondas reentrantes e fibrilação em tecido cardíaco, utilizando um novo modelo matemático." Universidade de São Paulo, 2005. http://www.teses.usp.br/teses/disponiveis/82/82131/tde-29032006-152336/.

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A fibrilação, atrial ou ventricular, é caracterizada por uma desorganização da atividade elétrica do músculo. O coração, que normalmente contrai-se globalmente, em uníssono e uniforme, durante a fibrilação contrai-se localmente em várias regiões, de modo descoordenado. Para estudar qualitativamente este fenômeno, é aqui proposto um novo modelo matemático, mais simples do que os demais existentes e que, principalmente, admite uma representação singela na forma de circuito elétrico equivalente. O modelo foi desenvolvido empiricamente, após estudo crítico dos modelos conhecidos, e após uma série

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15

Driver, David Philip. "An optimisation-based approach to FKPP-type equations." Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/277769.

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In this thesis, we study a class of reaction-diffusion equations of the form $\frac{\partial u}{\partial t} = \mathcal{L}u + \phi u - \tfrac{1}{k} u^{k+1}$ where $\mathcal{L}$ is the stochastic generator of a Markov process, $\phi$ is a function of the space variables and $k\in \mathbb{R}\backslash\{0\}$. An important example, in the case when $k > 0$, is equations of the FKPP-type. We also give an example from the theory of utility maximisation problems when such equations arise and in this case $k < 0$. We introduce a new representation, for the solution of the equation, as the optimal value

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16

Giletti, Thomas. "Phénomènes de propagation dans des milieux diffusifs excitables : vitesses d'expansion et systèmes avec pertes." Thesis, Aix-Marseille 3, 2011. http://www.theses.fr/2011AIX30043.

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Les systèmes de réaction-diffusion interviennent pour décrire les transitions de phase dans de nombreux champs d'application. Cette thèse porte sur l'analyse mathématique de modèles de propagation dans des milieux diffusifs, non bornés et hétérogènes, et s'inscrit ainsi dans la lignée d'une recherche particulièrement active. La première partie concerne l'équation simple: on s'y intéressera à la structure interne des fronts, mais on exhibera aussi de nouvelles dynamiques où la vitesse d'un profil de propagation n'est pas unique. Dans la seconde partie, on s'intéresse aux systèmes à deux équatio

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17

Doli, Valentin. "Phénomènes de propagation de champignons parasites de plantes par couplage de diffusion spatiale et de reproduction sexuée." Thesis, Rennes 1, 2017. http://www.theses.fr/2017REN1S139/document.

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On considère des organismes qui mixent reproduction sexuée et asexuée, dans une situation où la reproduction sexuée fait intervenir à la fois de la dispersion spatiale et de la limitation d'appariement. Nous proposons un modèle qui implique deux équations couplées, la première étant une équation différentielle ordinaire de type logistique, la seconde étant une équation de réaction-diffusion. Grâce à des valeurs réalistes des différents coefficients, il s'avère que la deuxième équation fait intervenir une échelle de temps rapide, alors que la première fait intervenir une échelle de temps lente.

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18

Ghazaryan, Anna R. "Nonlinear convective instability of fronts a case study /." Connect to resource, 2005. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1117552079.

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Thesis (Ph.D.)--Ohio State University, 2005.<br>Title from first page of PDF file. Document formatted into pages; contains ix, 176 p.; also includes graphics. Includes bibliographical references (p. 172-176). Available online via OhioLINK's ETD Center

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19

Alqawasmeh, Yousef. "Models for Persistence and Spread of Structured Populations in Patchy Landscapes." Thesis, Université d'Ottawa / University of Ottawa, 2017. http://hdl.handle.net/10393/36845.

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In this dissertation, we are interested in the dynamics of spatially distributed populations. In particular, we focus on persistence conditions and minimal traveling periodic wave speeds for stage-structured populations in heterogeneous landscapes. The model includes structured populations of two age groups, juveniles and adults, in patchy landscapes. First, we present a stage-structured population model, where we divide the population into pre-reproductive and reproductive stages. We assume that all parameters of the two age groups are piecewise constant functions in space. We derive expli

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20

Silva, Juliana Fernandes da. "Aplicações de semigrupos em sistemas de reação-difusão e a existência de ondas viajantes." Universidade de São Paulo, 2010. http://www.teses.usp.br/teses/disponiveis/45/45132/tde-31082010-093717/.

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Sistemas de reação-difusão têm sido largamente estudados em diferentes contextos e através de diferentes métodos, motivados pela sua constante aparição em modelos de interação em contextos químicos, biológicos e ainda em fenômenos ecológicos. Neste trabalho nos propomos a estudar existência e unicidade - tanto do ponto de vista local como global - de soluções para uma classe de sistemas de reação-difusão acoplados, denidos em R^2, utilizando como ferramenta a teoria de semigrupos de operadores lineares. Apresentamos dois importantes exemplos: o modelo de Rosenzweig-MacArthur e um particular ca

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21

Griette, Quentin. "Mathematical and numerical analysis of propagation models arising in evolutionary epidemiology." Thesis, Montpellier, 2017. http://www.theses.fr/2017MONTS051/document.

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Cette thèse porte sur différents modèles de propagation en épidémiologie évolutive. L'objectif est d'en faire une analyse mathématique rigoureuse puis d'en tirer des enseignements biologiques. Dans un premier temps nous envisageons le cas d'une population d'hôtes répartis de manière homogène dans un espace linéaire, dans laquelle se propage un pathogène pouvant muter entre deux phénotypes plus ou moins virulents. Ce phénomène de mutation est à l'origine d'une interaction entre les dynamiques évolutive et épidémiologique du pathogène. Nous étudions la vitesse de propagation de l'épidémie et l'e

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22

Shabala, Alexander. "Mathematical modelling of oncolytic virotherapy." Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:cca2c9bc-cbd4-4651-9b59-8a4dea7245d1.

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This thesis is concerned with mathematical modelling of oncolytic virotherapy: the use of genetically modified viruses to selectively spread, replicate and destroy cancerous cells in solid tumours. Traditional spatially-dependent modelling approaches have previously assumed that virus spread is due to viral diffusion in solid tumours, and also neglect the time delay introduced by the lytic cycle for viral replication within host cells. A deterministic, age-structured reaction-diffusion model is developed for the spatially-dependent interactions of uninfected cells, infected cells and virus par

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23

Kay, Alison Lindsey. "Travelling fronts and wave-trains in reaction-diffusion equations." Thesis, University of Warwick, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.342513.

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24

Meral, Gulnihal. "Numerical Solution Of Nonlinear Reaction-diffusion And Wave Equations." Phd thesis, METU, 2009. http://etd.lib.metu.edu.tr/upload/3/12610568/index.pdf.

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In this thesis, the two-dimensional initial and boundary value problems (IBVPs) and the one-dimensional Cauchy problems defined by the nonlinear reaction- diffusion and wave equations are numerically solved. The dual reciprocity boundary element method (DRBEM) is used to discretize the IBVPs defined by single and system of nonlinear reaction-diffusion equations and nonlinear wave equation, spatially. The advantage of DRBEM for the exterior regions is made use of for the latter problem. The differential quadrature method (DQM) is used for the spatial discretization of IBVPs and Cauchy problem

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25

Denman, Paula Kerri. "Modelling strategies for the healing of burn wounds." Queensland University of Technology, 2007. http://eprints.qut.edu.au/16433/.

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Epidermal wound healing requires the coordinated involvement of complex cellular and biochemical processes. In the case of epidermal wounds associated with burns, the healing process may be less than optimal and may take a significant amount of time, possibly resulting in infection and scarring. An innovative method to assist in the repair of the epidermis (the outer layer of skin) is to use an aerosolised apparatus. This method involves taking skin cells from an area of the patient's undamaged skin, culturing the cells in a laboratory, encouraging them to rapidly proliferate, then harvesti

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26

Crooks, Elaine Craig Mackay. "Travelling-wave solutions for parabolic systems." Thesis, University of Bath, 1996. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.319218.

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27

Zou, Xingfu. "Traveling wave solutions of delayed reaction-diffusion systems and lattice differential equations." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/nq22936.pdf.

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28

Roy, Christian. "The Origin of Wave Blocking for a Bistable Reaction-Diffusion Equation : A General Approach." Thèse, Université d'Ottawa / University of Ottawa, 2012. http://hdl.handle.net/10393/22704.

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Mathematical models displaying travelling waves appear in a variety of domains. These waves are often faced with different kinds of perturbations. In some cases, these perturbations result in propagation failure, also known as wave-blocking. Wave-blocking has been studied in the case of several specific models, often with the help of numerical tools. In this thesis, we will display a technique that uses symmetry and a center manifold reduction to find a criterion which defines regions in parameter space where a wave will be blocked. We focus on waves with low velocity and small symmetry-breaki

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Garnier, Jimmy. "Analyse mathématique de modèles de dynamique des populations : équations aux dérivées partielles paraboliques et équations intégro-différentielles." Phd thesis, Aix-Marseille Université, 2012. http://tel.archives-ouvertes.fr/tel-00755296.

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Cette thèse porte sur l'analyse mathématique de modèles de réaction-dispersion. L'objectif est de comprendre l'influence du terme de réaction, de l'opérateur de dispersion, et de la donnée initiale sur la propagation des solutions de ces équations. Nous nous sommes intéressés principalement à deux types d'équations de réaction-dispersion : les équations de réaction-diffusion où l'opérateur de dispersion différentielle est le laplacien et les équations intégro-différentielles pour lesquelles l'opérateur de dispersion est de type convolution. Dans le cadre des équations de réaction-diffusion en

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Nicola, Ernesto Miguel. "Interfaces between Competing Patterns in Reaction-diffusion Systems with Nonlocal Coupling." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2002. http://nbn-resolving.de/urn:nbn:de:swb:14-1036499969687-26395.

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In this thesis we investigate the formation of patterns in a simple activator-inhibitor model supplemented with an inhibitory nonlocal coupling term. This model exhibits a wave instability for slow inhibitor diffusion, while, for fast inhibitor diffusion, a Turing instability is found. For moderate values of the inhibitor diffusion these two instabilities occur simultaneously at a codimension-2 wave-Turing instability. We perform a weakly nonlinear analysis of the model in the neighbourhood of this codimension-2 instability. The resulting amplitude equations consist in a set of coupled Ginzbur

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Nicola, Ernesto Miguel. "Interfaces between Competing Patterns in Reaction-diffusion Systems with Nonlocal Coupling." Doctoral thesis, Technische Universität Dresden, 2001. https://tud.qucosa.de/id/qucosa%3A24181.

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In this thesis we investigate the formation of patterns in a simple activator-inhibitor model supplemented with an inhibitory nonlocal coupling term. This model exhibits a wave instability for slow inhibitor diffusion, while, for fast inhibitor diffusion, a Turing instability is found. For moderate values of the inhibitor diffusion these two instabilities occur simultaneously at a codimension-2 wave-Turing instability. We perform a weakly nonlinear analysis of the model in the neighbourhood of this codimension-2 instability. The resulting amplitude equations consist in a set of coupled Ginzbur

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32

Badke, Sven [Verfasser], Ben [Akademischer Betreuer] Schweizer, and Matthias [Gutachter] Röger. "Traveling wave solutions of reaction-diffusion equations with x-dependent combustion type nonlinearities / Sven Badke. Betreuer: Ben Schweizer. Gutachter: Matthias Röger." Dortmund : Universitätsbibliothek Dortmund, 2016. http://d-nb.info/111246770X/34.

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Chekroun, Abdennasser. "Contribution à l’analyse mathématique d’équations aux dérivées partielles structurées en âge et en espace modélisant une dynamique de population cellulaire." Thesis, Lyon, 2016. http://www.theses.fr/2016LYSE1040/document.

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Cette thèse s'inscrit dans le cadre général de l'étude de la dynamique de populations. Elle porte sur la modélisation et l'analyse mathématique de l'hématopoïèse, le processus de production et de régulation des cellules sanguines. La population de cellules est perçue comme un milieu continu avec une structuration en âge et en espace. Nous avons commencé par analyser des modèles d'équations différentielles et aux différences à retard discret et distribué. Ces modèles à retard permettent de mettre en évidence des comportements particuliers tels que l'existence de solutions périodiques. Ensuite,

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Wang, Jian. "From local to global: Complex behavior of spatiotemporal systems with fluctuating delay times." Doctoral thesis, Universitätsbibliothek Chemnitz, 2014. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-133734.

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The aim of this thesis is to investigate the dynamical behaviors of spatially extended systems with fluctuating time delays. In recent years, the study of spatially extended systems and systems with fluctuating delays has experienced a fast growth. In ubiquitous natural and laboratory situations, understanding the action of time-delayed signals is a crucial for understanding the dynamical behavior of these systems. Frequently, the length of the delay is found to change with time. Spatially extended systems are widely studied in many fields, such as chemistry, ecology, and biology. Self-organiz

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Wang, Jian. "From local to global: Complex behavior of spatiotemporal systems with fluctuating delay times: From local to global: Complex behavior of spatiotemporal systemswith fluctuating delay times." Doctoral thesis, Universitätsverlag der Technischen Universität Chemnitz, 2013. https://monarch.qucosa.de/id/qucosa%3A20006.

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The aim of this thesis is to investigate the dynamical behaviors of spatially extended systems with fluctuating time delays. In recent years, the study of spatially extended systems and systems with fluctuating delays has experienced a fast growth. In ubiquitous natural and laboratory situations, understanding the action of time-delayed signals is a crucial for understanding the dynamical behavior of these systems. Frequently, the length of the delay is found to change with time. Spatially extended systems are widely studied in many fields, such as chemistry, ecology, and biology. Self-organiz

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李宜展. "Traveling Waves of Autocatalytic Reaction-Diffusion Systems." Thesis, 2008. http://ndltd.ncl.edu.tw/handle/4mn79p.

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Lin, Jian-Jhong, and 林建仲. "Traveling Waves for Reaction-Diffusion Partial Difference Systems." Thesis, 2011. http://ndltd.ncl.edu.tw/handle/99925751504913528341.

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博士<br>國立清華大學<br>數學系<br>99<br>In this thesis, we mainly discuss the existence of the traveling wave solutions for reaction-diffusion type partial difference systems. In particular, we pay attention to the following four models: (1) reaction-diffusion equation with linear diffusion and linear reaction term, (2) reaction-diffusion equation with linear diffusion and polynomial reaction term, (3) discretization of λ-ω system, and (4) discretization of RTD-based cellular neural networks. For models (1), (2) and (3), we consider their “periodic traveling wave” solutions; and for model (4), we conside

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Kung, Shih-Yin, and 龔詩尹. "On the Patterns and waves in reaction-diffusion equations." Thesis, 2011. http://ndltd.ncl.edu.tw/handle/20842421073664418059.

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博士<br>國立彰化師範大學<br>數學系所<br>99<br>This thesis deals with patterns and waves in FitzHugh-Nagumo type reaction-diffusion systems . We use variational approach to investigate Turing patterns and various types of standing waves . In the study of standing waves joining with two equilibria ,we obtain heteroclinic orbits of certain Hamiltonian systems .We further consider heteroclinic orbits of elliptic partial differential equations on infinite cylinders . Of particular interest is standing wave joining with Turing patterns .

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Miller, Patrick David. "Stability of travelling waves for a three-component reaction-diffusion system." 1994. https://scholarworks.umass.edu/dissertations/AAI9510507.

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This paper investigates a reaction-diffusion system modeling three competing species, with diffusion in one space dimension. The main result is the existence and asymptotic stability of a travelling wave connecting two stable equilibria. The results are obtained in a small parameter regime where two of the species diffuse very slowly. Singular perturbation methods are used to locate the connecting solution, and the existence for positive values of the perturbation parameter is established via the connection index of Conley. The stability result applies geometric and topological methods develop

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Chien, Hong-yu, and 簡鴻宇. "Periodic Traveling Waves of a Reaction Diffusion Equation with Non-local Nonlinearity." Thesis, 2012. http://ndltd.ncl.edu.tw/handle/94260452131979069207.

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碩士<br>國立臺灣大學<br>數學研究所<br>100<br>In this article, the reaction-diffusion equation arising from population dynamics with Fisher-type non-local consumptions defined through an interaction integral kernel is concerned. In order to know the impact of the integral kernels on the solutions, we try and expect that there exist some non-typical traveling waves different from waves of the classical Fisher equation. Through the bifurcation and perturbation methods, we can generate periodic traveling waves of these equations for the asymmetric integral kernels. By the way, to make the result complete, the

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Chien, Hung-Yu, and 簡鴻宇. "Variational Approaches to Three-Phase Standing and Traveling Waves of Reaction-Diffusion-Gradient Systems with a Triple-Well Potential." Thesis, 2019. http://ndltd.ncl.edu.tw/handle/5x7h4w.

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博士<br>國立臺灣大學<br>數學研究所<br>107<br>In this paper we aim to find standing and traveling wave solutions, i.e. w(z, y) = u(x, y, t) with z = x − ct, to the reaction-diffusion gradient system with a triple- well potential ∂tu = ∆u − ∇W(u) on an entire domain R2 or a cylindrical domain R×(−l,l). Firstly by the theory of Γ-convergence, standing wave solutions (i.e. stationary solutions) are obtained under a condition that the potential W is invariant under a simple reflection. This symmetry assumption is weaker than the invariance under a general symmetric group, which is assumed by some literatures. A

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Bino, George Ashish. "Eco-evolutionary dynamics of microbial communities with heterogeneous growth and dispersal." Thesis, 2020. https://hdl.handle.net/2144/41998.

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Understanding eco-evolutionary dynamics in cancer tumors, species invasions, and the human microbiome is vital for numerous health and economic applications. However, spatial structure and population heterogeneity make this challenging. This dissertation tackles these challenges using a population dynamics approach, wherein systems evolve through individual growth and dispersal. The bulk of this dissertation studies expanding populations, such as growing microbial colonies, species range expansions, and cancer tumors. In this context, I first study the effect of a directional bias in dispe

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Chiou, Yu-Sheng, and 裘愉生. "Travelling Wave Solutions for Reaction-Diffusion-Advection Equations." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/58061221519913587970.

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碩士<br>臺灣大學<br>數學研究所<br>98<br>There are two parts in this paper. Part I is concerned with the travelling wave solutions for reaction-diffusion-advection equations . We consider periodic advection and combustion, monostable nonlinear reaction term . We mainly survey the results of existence, uniqueness, and monotonicity of pulsating waves from the paper by Berestycki and Hamel [1]. Part II deals with exact travelling wave solutions of competitive Lotka-Volterra systems of three species.

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Chang, Yuan-Ting, and 張菀庭. "Nonplanar Traveling Wave Solutions of Reaction-Diffusion Equations." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/57526300100281149557.

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碩士<br>國立臺灣大學<br>數學研究所<br>98<br>We are dealing with traveling wave solutions of a reaction-diffusion equation ut=△u+uzz-f(u), where (x, z)=(x1,---, xn, z) ∈Rn+1 is the space variable and △ is the Laplacian in Rn. Assume that f(u) is a bistable nonlinear, then we consider the balanced case and unbalanced case respectively. In the preceding case, we describe some types of traveling waves connecting two stable equilibria. In the case of latter, we want to find out the bistable-type traveling waves with the interfaces other than plane. If the solution is restricted to be cylindrically symmetric, th

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Cheung, Anthea. "Spatiotemporal patterns in the wake of traveling wave solutions to the Morris-Lecar model of neural tissue." Thesis, 2019. https://hdl.handle.net/2144/37380.

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In this dissertation, we discuss spatiotemporal patterns in the wake of traveling waves in a microelectrode array (MEA) recording of a human epileptic seizure. In chapter two, we describe a method for estimating the direction of planar waves found in the last third of the seizure. We categorize the different phenomena that occur during those waves when projected along a one-dimensional slice in the domain. In chapter three, we summarize known examples of patterns in the wake of traveling wave solutions to reaction-diffusion systems. A brief review of results regarding the spectral stability

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Hsia, Chun-Hsiung, and 夏俊雄. "Traveling Wave Solutions of Reaction-Diffusion Equations and The Method o f Continuity." Thesis, 1999. http://ndltd.ncl.edu.tw/handle/33982583194209825229.

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碩士<br>國立臺灣大學<br>數學研究所<br>87<br>Reaction-Diffusion equations describe many models in mathematics,physics,chemistry,biology. For example, see D. J. Murray [7]. One of the most interesting discoveries in studying R-D equations is that traveling wave solutions not only appear in hyperbolic equations but also in parabolic equations. And traveling wave solutions are always important solutions, We divide this paper into two parts. In the first part, we describe maximum principles, stability, existence, uniqueness, uniform convergence of traveling wave solutions of one dimensional R-D equat

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Yang, Chi-Ru, and 楊其儒. "Geometric Approach to the Existence of Traveling Wave Solutions for Reaction Diffusion Systems." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/73765219133671672078.

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博士<br>國立交通大學<br>應用數學系所<br>98<br>This dissertation investigates the existence of traveling wave solutions in Reaction Diffusion system using geometric approach. The first part of the dissertation applies the geometric singular perturbation to establish the diversity of traveling wave solutions of a FitzHugh-Nagumo type equation with turning point. There coexist different front of traveling wave and we give a complete classification for all of these fronts of traveling waves. The second part of the dissertation applies high-dimensional phase space analysis together with Wazewski Theorem and LaSa

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