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1

He, Taiping. "Reaction-Diffusion Systems with Discontinuous Reaction Functions." NCSU, 2005. http://www.lib.ncsu.edu/theses/available/etd-03192005-101102/.

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This dissertation studies coupled reaction diffusion systems with discontinuous reaction functions. It includes three parts: The first part is concerned with the existence of solutions for a coupled system of two parabolic equations and the second part is devoted to the monotone iterative methods for monotone and mixed quasimonotone functions. Various monotone iterative schemes are presented and each of these schemes leads to an existence-comparison theorem and the monotone convergence of the maximal and minimal sequences. In the third part, the monotone iterative schemes are applied to comput
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2

Yangari, Sosa Miguel Ángel. "Fractional reaction-diffusion problems." Tesis, Universidad de Chile, 2014. http://www.repositorio.uchile.cl/handle/2250/115538.

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Doctor en Ciencias de la Ingeniería, Mención Modelación Matemática<br>This thesis deals with two different problems: in the first one, we study the large-time behavior of solutions of one-dimensional fractional Fisher-KPP reaction diffusion equations, when the initial condition is asymptotically front-like and it decays at infinity more slowly than a power x^b, where b < 2\alpha and \alpha\in (0,1) is the order of the fractional Laplacian (Chapter 2); in the second problem, we study the time asymptotic propagation of solutions to the fractional reaction diffusion cooperative systems (Chapter 3
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3

Yangari, Sosa Miguel Angel. "Fractional reaction-diffusion problems." Toulouse 3, 2014. http://thesesups.ups-tlse.fr/2270/.

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Cette thèse porte sur deux problèmes différents : dans le premier, nous étudions le comportement en temps long des solutions des équations de réaction diffusion 1d-fractionnaire de type Fisher-KPP lorsque la condition initiale est asymptotiquement de type front et décroît à l'infini plus lentement que, où et est l'indice du laplacien fractionnaire (Chapitre 2). Dans le second problème, nous étudions la propagation asymptotique en temps des solutions de systèmes coopératifs de réaction-diffusion (Chapitre 3). Dans le premier problème, nous démontrons que les ensembles de niveau des solutions se
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4

Coulon, Anne-Charline. "Propagation in reaction-diffusion equations with fractional diffusion." Doctoral thesis, Universitat Politècnica de Catalunya, 2014. http://hdl.handle.net/10803/277576.

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This thesis focuses on the long time behaviour of solutions to Fisher-KPP reaction-diffusion equations involving fractional diffusion. This type of equation arises, for example, in spatial propagation or spreading of biological species (rats, insects,...). In population dynamics, the quantity under study stands for the density of the population. It is well-known that, under some specific assumptions, the solution tends to a stable state of the evolution problem, as time goes to infinity. In other words, the population invades the medium, which corresponds to the survival of the species,
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5

Benson, Debbie Lisa. "Reaction diffusion models with spatially inhomogeneous diffusion coefficients." Thesis, University of Oxford, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.239337.

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6

Fei, Ning Fei. "Studies in reaction-diffusion equations." Thesis, Heriot-Watt University, 2003. http://hdl.handle.net/10399/310.

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7

Grant, Koryn. "Symmetries and reaction-diffusion equations." Thesis, University of Kent, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.264601.

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8

Frömberg, Daniela. "Reaction Kinetics under Anomalous Diffusion." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät I, 2011. http://dx.doi.org/10.18452/16374.

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Die vorliegende Arbeit befasst sich mit der Verallgemeinerung von Reaktions-Diffusions-Systemen auf Subdiffusion. Die subdiffusive Dynamik auf mesoskopischer Skala wurde mittels Continuous-Time Random Walks mit breiten Wartezeitverteilungen modelliert. Die Reaktion findet auf mikroskopischer Skala, d.h. während der Wartezeiten, statt und unterliegt dem Massenwirkungsgesetz. Die resultierenden Integro-Differentialgleichungen weisen im Integralkern des Transportterms eine Abhängigkeit von der Reaktion auf. Im Falle der Degradation A->0 wurde ein allgemeiner Ausdruck für die Lösungen beliebiger D
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9

Coulon, Chalmin Anne-Charline. "Fast propagation in reaction-diffusion equations with fractional diffusion." Toulouse 3, 2014. http://thesesups.ups-tlse.fr/2427/.

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Cette thèse est consacrée à l'étude du comportement en temps long, et plus précisément de phénomènes de propagation rapide, des équations de réaction-diffusion de type Kisher-KPP avec diffusion fractionnaire. Ces équations modélisent, par exemple, la propagation d'espèces biologiques. Sous certaines hypothèses, la population envahit le milieu et nous voulons comprendre à quelle vitesse cette invasion a lieu. Pour répondre à cette question, nous avons mis en place une nouvelle méthode et nous l'appliquons à différents modèles. Dans une première partie, nous étudions deux problèmes d'évolution c
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10

Coville, Jerome. "Equations de reaction diffusion non-locale." Phd thesis, Université Pierre et Marie Curie - Paris VI, 2003. http://tel.archives-ouvertes.fr/tel-00004313.

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Cette thèse est consacrée à l'étude des équations de réaction diffusion non-locale du type $u_(t)-(\int_(\R)J(x-y)[u(y)-u(x)]dy)=f(u)$. Ces équations non-linéaires apparaissent naturellement en physique et en biologie. On s'intéresse plus particulièrement aux propriétés (existence, unicité, monotonie) des solutions du type front progressif. Trois classes de non-linéarités $f$ (bistable, ignition, monostable) sont étudiées. L'existence dans les cas bistable et ignition est obtenue via une technique d'homotopie. Le cas monostable nécessite une autre approche. L'existence est obtenue via une appr
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11

Bishop, Donald Paul. "Diffusion-based microalloying via reaction sintering." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/nq39320.pdf.

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12

Hemming, Christopher John. "Resonantly forced inhomogeneous reaction-diffusion systems." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape3/PQDD_0022/MQ50344.pdf.

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13

Lunney, Michael E. "Numerical dynamics of reaction-diffusion equations." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp02/NQ61659.pdf.

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14

Bradshaw-Hajek, Bronwyn. "Reaction-diffusion equations for population genetics." Access electronically, 2004. http://www.library.uow.edu.au/adt-NWU/public/adt-NWU20041221.160902/index.html.

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15

Hellander, Stefan. "Stochastic Simulation of Reaction-Diffusion Processes." Doctoral thesis, Uppsala universitet, Avdelningen för beräkningsvetenskap, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-198522.

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Numerical simulation methods have become an important tool in the study of chemical reaction networks in living cells. Many systems can, with high accuracy, be modeled by deterministic ordinary differential equations, but other systems require a more detailed level of modeling. Stochastic models at either the mesoscopic level or the microscopic level can be used for cases when molecules are present in low copy numbers. In this thesis we develop efficient and flexible algorithms for simulating systems at the microscopic level. We propose an improvement to the Green's function reaction dynamics
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16

Tang, François-David. "Reaction-diffusion fronts in heterogeneous combustion." Thesis, McGill University, 2011. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=104561.

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Heterogeneous flames are modeled in a simplified system where the fuel particles are discrete heat sources embedded in an inert, heat conducting medium. Two asymptotic regimes of flame propagation are found and exhibit differences in both the propagation limits and the front speeds. When the flame thickness is much larger than the characteristic particle spacing, the media containing the sources can be approximated as homogeneous in the reaction zone. In this case, the propagation of the front is defined as being in the continuum regime. In contrast, when the front thickness is on the same sca
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17

Stapley, Andrew G. F. "Diffusion & reaction in wheat chains." Thesis, University of Cambridge, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.390002.

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18

Crampin, Edmund John. "Reaction-diffusion patterns on growing domains." Thesis, University of Oxford, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.325756.

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19

Smith, Stephen. "Stochastic reaction-diffusion models in biology." Thesis, University of Edinburgh, 2018. http://hdl.handle.net/1842/33142.

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Every cell contains several millions of diffusing and reacting biological molecules. The interactions between these molecules ultimately manifest themselves in all aspects of life, from the smallest bacterium to the largest whale. One of the greatest open scientific challenges is to understand how the microscopic chemistry determines the macroscopic biology. Key to this challenge is the development of mathematical and computational models of biochemistry with molecule-level detail, but which are sufficiently coarse to enable the study of large systems at the cell or organism scale. Two such mo
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20

Pfeifer, Peter, and Chen Hou. "Diffusion-Reaction in space-filling networks." Universitätsbibliothek Leipzig, 2015. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-184563.

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21

Nagaiah, Chamakuri. "Adaptive numerical simulation of reaction-diffusion systems." [S.l.] : [s.n.], 2007. http://deposit.ddb.de/cgi-bin/dokserv?idn=985277882.

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22

Claus, Isabelle. "Microscopic chaos, fractals, and reaction-diffusion processes." Doctoral thesis, Universite Libre de Bruxelles, 2002. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/211441.

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23

Sun, Xiaodi. "Metastable dynamics of convection-diffusion-reaction equations." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/tape15/PQDD_0002/NQ34630.pdf.

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24

Rondoni, Lamberto. "A stochastic treatment of reaction and diffusion." Diss., This resource online, 1991. http://scholar.lib.vt.edu/theses/available/etd-07282008-134042/.

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25

Santos, Jaime Eduardo Moutinho. "Non-equilibrium dynamics of reaction-diffusion processes." Thesis, University of Oxford, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.361994.

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26

Furtado, Kalli. "Mesoscopic simulations of reaction-diffusion-advection problems." Thesis, University of Oxford, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.442953.

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27

Davidson, Fordyce A. "Bifurcation in systems of reaction-diffusion equations." Thesis, Heriot-Watt University, 1993. http://hdl.handle.net/10399/1444.

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28

Freitas, Pedro S. C. de. "Some problems in nonlocal reaction-diffusion equations." Thesis, Heriot-Watt University, 1994. http://hdl.handle.net/10399/1401.

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29

Howard, Martin. "Non-equilibrium dynamics of reaction-diffusion systems." Thesis, University of Oxford, 1996. http://ora.ox.ac.uk/objects/uuid:4485a178-6262-4487-b40f-7c7ec790d687.

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Fluctuations are known to radically alter the behaviour of reaction-diffusion systems. Below a certain upper critical dimension d<sub>c</sub> , this effect results in the breakdown of traditional approaches, such as mean field rate equations. In this thesis we tackle this fluctuation problem by employing systematic field theoretic/renormalisation group methods, which enable perturbative calculations to be made below d<sub>c</sub>. We first consider a steady state reaction front formed in the two species irreversible reaction A + B → Ø. In one dimension we demonstrate that there are two compone
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30

Turpin, Kevin. "Patterns and fronts in reaction-diffusion systems." Thesis, University of Nottingham, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.287233.

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31

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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32

Kammogne, Kamgaing Rodrigue. "Domain decomposition methods for reaction-diffusion systems." Thesis, University of Birmingham, 2014. http://etheses.bham.ac.uk//id/eprint/4599/.

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Domain Decomposition (DD) methods have been successfully used to solve elliptic problems, as they deal with them in a more elegant and efficient way than other existing numerical methods. This is achieved through the division of the domain into subdomains, followed by the solving of smaller problems within these subdomains which leads to the solution. Furthermore DD-techniques can incorporate in their implementation not only the physics of the different phenomena associated with the modeling, but also the enhancement of parallel computing. They can be divided into two major categories: with an
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33

Agliari, Elena, Raffaella Burioni, Davide Cassi, and Franco M. Neri. "Autocatalytic reaction-diffusion processes in restricted geometries." Universitätsbibliothek Leipzig, 2016. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-192966.

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34

Mahmutovic, Anel. "Reaction-Diffusion kinetics of Protein DNA Interactions." Doctoral thesis, Uppsala universitet, Beräknings- och systembiologi, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-263527.

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Transcription factors need to rapidly find one specific binding site among millions of nonspecific sites on the chromosomal DNA. In this thesis I use various aspects of reaction-diffusion theory to investigate the interaction between proteins and DNA and to explain the searching, finding and binding to specific operator sites. Using molecular dynamics methods we calculate the free energy profile for the model protein LacI as it leaves a nonspecific stretch of DNA and as it slides along DNA. Based on the free energy profiles we estimate the microscopic dissociation rate constant, kdmicro ~1.45×
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35

Agliari, Elena, Raffaella Burioni, Davide Cassi, and Franco M. Neri. "Autocatalytic reaction-diffusion processes in restricted geometries." Diffusion fundamentals 7 (2007) 1, S. 1-8, 2007. https://ul.qucosa.de/id/qucosa%3A14157.

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36

Van, Wijland Frédéric. "Marches aleatoires et problemes de reaction-diffusion." Paris 11, 1998. http://www.theses.fr/1998PA112008.

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Cette these comprend deux parties. La premiere est consacree a l'etude de quelques proprietes de la marche aleatoire simple, la seconde traite des reactions limitees par diffusion avec transition de phase dans l'etat stationnaire. Dans la partie traitant de la marche aleatoire simple, l'objet central de l'etude est le support de la marche, c'est-a-dire l'ensemble des sites visites. Nous considerons en detail les proprietes topologiques du support d'une marche bidimensionnelle. Combien y a-t-il d'ilots de sites non visites enfermes dans le support apres un grand nombre de pas ? quelle est la lo
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37

Yu, Weiming. "Identification of Coefficients in Reaction-Diffusion Equations." University of Cincinnati / OhioLINK, 2004. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1076186036.

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38

Al-Ofl, Abdalaziz Saleem. "Analysis of complex nonlinear reaction-diffusion equations." Thesis, Durham University, 2008. http://etheses.dur.ac.uk/2422/.

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A mathematical analysis has been carried out for some nonlinear reaction- diffusion equations on open bounded convex domains Ω C R(^d)(d < 3) with Robin boundary conditions- Existence, uniqueness and continuous dependence on initial data of weak and strong solutions are proved. A numerical analysis has also been undertaken for these nonlinear reaction- diffusion equations on the above domains. A fully practical piecewise linear finite element approximation is proposed for which existence and uniqueness of the numerical solution are proved. Semi-discrete and fully discrete error estimates are g
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39

Hagberg, Aric Arild. "Fronts and patterns in reaction-diffusion equations." Diss., The University of Arizona, 1994. http://hdl.handle.net/10150/186901.

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This is a study of fronts and patterns formed in reaction-diffusion systems. A doubly-diffusive version of the two component FitzHugh-Nagumo equations with bistable reaction dynamics is investigated as an abstract model for the study of pattern phenomenologies found in many different physical systems. Front solutions connecting the two stable uniform states are found to be key building blocks for understanding extended patterns such as stationary domains and traveling pulses in one dimension, and labyrinthine structures, splitting spots, and spiral wave turbulence in two dimensions. The number
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40

Poole, Anthony John. "Reaction-diffusion structures in nonlinear chemical kinetics." Thesis, University of Leeds, 1998. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.712528.

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41

Datar, A. S. "Studies of reaction diffusion in porous catalysts." Thesis(Ph.D.), CSIR-National Chemical Laboratory, Pune, 1985. http://dspace.ncl.res.in:8080/xmlui/handle/20.500.12252/3231.

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42

Burke, Meghan A. "Suicide substrates : an analysis of the enzyme reaction and reaction-diffusion equations." Thesis, University of Oxford, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.305420.

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43

Filho, Sergio Muniz Oliva. "Reaction-diffusion systems on domains with thin channels." Diss., Georgia Institute of Technology, 1993. http://hdl.handle.net/1853/28837.

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44

Rolland, Guillaume. "Global existence and fast-reaction limit in reaction-diffusion systems with cross effects." Phd thesis, École normale supérieure de Cachan - ENS Cachan, 2012. http://tel.archives-ouvertes.fr/tel-00785757.

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This thesis is devoted to the study of parabolic systems of partial differential equations arising in mass action kinetics chemistry, population dynamics and electromigration theory. We are interested in the existence of global solutions, uniqueness of weak solutions, and in the fast-reaction limit in a reaction-diffusion system. In the first chapter, we study two cross-diffusion systems. We are first interested in a population dynamics model, where cross effects in the interactions between the different species are modeled by non-local operators. We prove the well-posedness of the correspondi
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45

Büger, Matthias. "Systems of reaction-diffusion equations and their attractors." Giessen : Selbstverlag des Mathematischen Instituts, 2005. http://catalog.hathitrust.org/api/volumes/oclc/62216537.html.

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46

Stich, Michael. "Target patterns and pacemakers in reaction-diffusion systems." [S.l.] : [s.n.], 2003. http://deposit.ddb.de/cgi-bin/dokserv?idn=967163943.

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47

Provatas, Nikolas. "Kinetic roughening and bifurcations in reaction-diffusion systems." Thesis, McGill University, 1994. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=28886.

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We study the dynamics of two reaction-diffusion phenomena driven by chemical activation and thermal dissipation and evolving, respectively, on a randomly distributed or continuous medium. The first system describes the process of slow combustion of a randomly distributed reactant. It is studied by a phase-field model built up from first principles and describes the evolution of thermal and reactant concentration fields. Our combustion model incorporates thermal diffusion, activation and dissipation. We examine it in a manner which makes a connection between the propagation of combustion fronts
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48

Xu, Lu. "Large deviations technique on stochastic reaction-diffusion equations." Thesis, University of Warwick, 2008. http://wrap.warwick.ac.uk/2736/.

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There are two different problems studied in this thesis. The first one is a travelling wave problem. We will improve the result proved in [4] to derive the ergodic property of the travelling wave behind the wavefront. The second problem is a large deviation problem concerning solutions to certain kind stochastic partial differential equations. We will first briefly introduce some basics about SPDE in chapter 2. In chapter 3, we will prove a large deviation principle for super-Brownian motion when it is considered as a solution to an SPDE, using the LDP for super-Brownian motion when it is cons
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49

Huang, Ke. "Diffusion and reaction in selected uranium alloy system." Doctoral diss., University of Central Florida, 2012. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/5311.

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U-Mo metallic fuels with Al alloys as the matrix/cladding are being developed as low enriched uranium fuels under the Reduced Enrichment for Research and Test Reactor (RERTR) program. Significant interactions have been observed to occur between the U-Mo fuel and the Al alloy during fuel processing and irradiation. U-Zr metallic fuels with stainless steel claddings have been developed for the generation IV sodium fast reactor (SFR). The fuel cladding chemical interaction (FCCI) induced by the interdiffusion of components was also observed. These interactions induce deleterious effects on the f
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50

Wu, Yixiang. "Long Time Behavior for Reaction-Diffusion Population Models." Thesis, University of Louisiana at Lafayette, 2016. http://pqdtopen.proquest.com/#viewpdf?dispub=10002390.

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<p> In this work, we study the long time behavior of reaction-diffusion models arising from mathematical biology. First, we study a reaction-diffusion population model with time delay. We establish a comparison principle for coupled upper/lower solutions, prove the existence/uniqueness result for the model, and show the global asymptotic behavior of the model by constructing successive improved upper/lower solutions. Next, we consider a reaction-diffusion equation with continuous delay and spatial variable coefficients. We prove the global attractivity of the positive steady state by showing t
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