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Dissertations / Theses on the topic 'Diffusion equations'

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Published: 4 June 2021

Last updated: 25 July 2025

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1

Ta, Thi nguyet nga. "Sub-gradient diffusion equations." Thesis, Limoges, 2015. http://www.theses.fr/2015LIMO0137/document.

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Ce mémoire de thèse est consacrée à l'étude des problèmes d'évolution où la dynamique est régi par l'opérateur de diffusion de sous-gradient. Nous nous intéressons à deux types de problèmes d'évolution. Le premier problème est régi par un opérateur local de type Leray-Lions avec un domaine borné. Dans ce problème, l'opérateur est maximal monotone et ne satisfait pas la condition standard de contrôle de la croissance polynomiale. Des exemples typiques apparaît dans l'étude de fluide non-Neutonian et aussi dans la description de la dynamique du flux de sous-gradient. Pour étudier le problème nou

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2

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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3

Prehl, Janett. "Diffusion on fractals and space-fractional diffusion equations." Doctoral thesis, Universitätsbibliothek Chemnitz, 2010. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-201001068.

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Ziel dieser Arbeit ist die Untersuchung der Sub- und Superdiffusion in fraktalen Strukturen. Der Fokus liegt auf zwei separaten Ansätzen, die entsprechend des Diffusionbereiches gewählt und variiert werden. Dadurch erhält man ein tieferes Verständnis und eine bessere Beschreibungsweise für beide Bereiche. Im ersten Teil betrachten wir subdiffusive Prozesse, die vor allem bei Transportvorgängen, z. B. in lebenden Geweben, eine grundlegende Rolle spielen. Hierbei modellieren wir den fraktalen Zustandsraum durch endliche Sierpinski Teppiche mit absorbierenden Randbedingungen und lösen dann die Ma

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4

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

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5

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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6

Ninomiya, Hirokazu. "Separatrices of competition-diffusion equations." 京都大学 (Kyoto University), 1995. http://hdl.handle.net/2433/187159.

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本文データは平成22年度国立国会図書館の学位論文(博士)のデジタル化実施により作成された画像ファイルを基にpdf変換したものである.<br>Kyoto Journal of Mathematics, vol35(3), pp.539-567, 1995, http://projecteuclid.org/euclid.kjm/1250518709<br>Kyoto University (京都大学)<br>0048<br>新制・課程博士<br>博士(理学)<br>甲第5884号<br>理博第1591号<br>新制||理||889(附属図書館)<br>UT51-95-D203<br>京都大学大学院工学研究科数学専攻<br>(主査)教授西田孝明, 教授渡辺信三, 教授岩崎敷久<br>学位規則第4条第1項該当

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7

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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8

Knaub, Karl R. "On the asymptotic behavior of internal layer solutions of advection-diffusion-reaction equations /." Thesis, Connect to this title online; UW restricted, 2001. http://hdl.handle.net/1773/6772.

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9

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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10

Cifani, Simone. "On nonlinear fractional convection - diffusion equations." Doctoral thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for matematiske fag, 2011. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-15192.

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11

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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12

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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13

Parvin, S. "Diffusion-convection problems in parabolic equations." Thesis, University of Manchester, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.382761.

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14

Coville, Jérôme. "Equations de réaction-diffusion non-locale." Paris 6, 2003. https://tel.archives-ouvertes.fr/tel-00004313.

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15

Cinti, Eleonora <1982&gt. "Bistable elliptic equations with fractional diffusion." Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2010. http://amsdottorato.unibo.it/3073/1/Cinti-Eleonora-Tesi.pdf.

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This work concerns the study of bounded solutions to elliptic nonlinear equations with fractional diffusion. More precisely, the aim of this thesis is to investigate some open questions related to a conjecture of De Giorgi about the one-dimensional symmetry of bounded monotone solutions in all space, at least up to dimension 8. This property on 1-D symmetry of monotone solutions for fractional equations was known in dimension n=2. The question remained open for n>2. In this work we establish new sharp energy estimates and one-dimensional symmetry property in dimension 3 for certain solu

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16

Cinti, Eleonora <1982&gt. "Bistable elliptic equations with fractional diffusion." Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2010. http://amsdottorato.unibo.it/3073/.

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This work concerns the study of bounded solutions to elliptic nonlinear equations with fractional diffusion. More precisely, the aim of this thesis is to investigate some open questions related to a conjecture of De Giorgi about the one-dimensional symmetry of bounded monotone solutions in all space, at least up to dimension 8. This property on 1-D symmetry of monotone solutions for fractional equations was known in dimension n=2. The question remained open for n>2. In this work we establish new sharp energy estimates and one-dimensional symmetry property in dimension 3 for certain solu

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17

Endal, Jørgen. "Nonlinear fractional convection-diffusion equations, with nonlocal and nonlinear fractional diffusion." Thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for matematiske fag, 2013. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-22955.

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We study nonlinear fractional convection-diffusion equations with nonlocal and nonlinear fractional diffusion. By the idea of Kru\v{z}kov (1970), entropy sub- and supersolutions are defined in order to prove well-posedness under the assumption that the solutions are elements in $L^{\infty}(\mathbb{R}^d\times (0,T))\cap C([0,T];L_\text{loc}^1(\mathbb{R}^d))$. Based on the work of Alibaud (2007) and Cifani and Jakobsen (2011), a local contraction is obtained for this type of equations for a certain class of L\'evy measures. In the end, this leads to an existence proof for initial data in $L

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18

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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19

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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20

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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21

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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22

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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23

Cardanobile, Stefano. "Diffusion systems and heat equations on networks." [S.l. : s.n.], 2008. http://nbn-resolving.de/urn:nbn:de:bsz:289-vts-64278.

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24

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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25

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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26

Meiler, Maria. "Analytic advances in difference equations of diffusion processes /." Göttingen : Sierke, 2009. http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&doc_number=017611057&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA.

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27

Lin, Xue Lei. "Separable preconditioner for time-space fractional diffusion equations." Thesis, University of Macau, 2017. http://umaclib3.umac.mo/record=b3691377.

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28

Sionoid, Peadar N. "Nonlinear wave equations with diffusion, diffraction and dispersion." Thesis, University of Cambridge, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.319935.

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29

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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30

Meiler, Maria. "Analytic advances in difference equations of diffusion processes." Göttingen Sierke, 2008. http://d-nb.info/992791685/04.

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31

Ferguson, R. C. "Numerical techniques for the drift-diffusion semiconductor equations." Thesis, University of Bath, 1996. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.362239.

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32

Carter, David, Boguslaw Kruczek, and F. Handan Tezel. "Application of Maxwell Stefan equations to characterize silicalite membranes." Universitätsbibliothek Leipzig, 2016. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-198056.

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33

Ding, Weiwei. "Propagation phenomena of integro-difference equations and bistable reaction-diffusion equations in periodic habitats." Thesis, Aix-Marseille, 2014. http://www.theses.fr/2014AIXM4737.

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Cette thèse concerne les phénomènes de propagation de certaines équations d'évolution dans des habitats périodiques. Dans la première partie, nous étudions les phénomènes d'expansion de certaines équations d'intégro-différence spatialement périodiques. Tout d'abord, nous établissons une théorie générale sur l'existence des vitesses de propagation pour des systèmes d'évolution noncompacts, sous l'hypothèse que les systèmes linéarisés ont des valeurs propres principales. Ensuite, nous introduisons la notion d'irréductibilité uniforme des mesures de Radon finies sur le cercle. On démontre que tou

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34

Wei, Hui Qin. "Preconditioners for solving fractional diffusion equations with discontinuous coefficients." Thesis, University of Macau, 2017. http://umaclib3.umac.mo/record=b3691375.

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35

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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36

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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37

Ryan, John Maurice-Car. "Global existence of reaction-diffusion equations over multiple domains." Texas A&M University, 2004. http://hdl.handle.net/1969.1/3312.

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Systems of semilinear parabolic differential equations arise in the modelling of many chemical and biological systems. We consider m component systems of the form ut = DΔu + f (t, x, u) ∂uk/∂η =0 k =1, ...m where u(t, x)=(uk(t, x))mk=1 is an unknown vector valued function and each u0k is zero outside Ωσ(k), D = diag(dk)is an m Ã m positive deﬁnite diagonal matrix, f : R Ã RnÃ Rm → Rm, u0 is a componentwise nonnegative function, and each Ωi is a bounded domain in Rn where ∂Ωi is a C2+αmanifold such that Ωi lies locall

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38

Wang, Shuyu. "Reaction-diffusion equations and the Laplacian in Hilbert space." Thesis, University of Ottawa (Canada), 1990. http://hdl.handle.net/10393/5772.

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This dissertation consists of two parts. First, we study some problems associated with reaction-diffusion equations with variables in finite-dimensional space. We investigate the positivity of solutions, the existence of positive invariant regions, and we also make some stability analysis. In part II, we study the Levy-Laplacian in infinite-dimensional space. We explore some properties of this Laplacian and solve some boundary value problems.

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39

Baugh, James Emory. "Group analysis of a system of reaction-diffusion equations." Thesis, Georgia Institute of Technology, 1991. http://hdl.handle.net/1853/28554.

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40

Hill, Adrian T. "Attractors for convection-diffusion equations and their numerical approximation." Thesis, University of Oxford, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.314907.

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41

Qu, Lei, and 瞿磊. "Multiplicity and stability of two-dimensional reaction-diffusion equations." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2001. http://hub.hku.hk/bib/B31226656.

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42

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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43

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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44

Vafadari, Cyrus. "Monte Carlo methods for parallel processing of diffusion equations." Thesis, Massachusetts Institute of Technology, 2013. http://hdl.handle.net/1721.1/82451.

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Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Nuclear Science and Engineering, 2013.<br>"June 2013." Cataloged from PDF version of thesis.<br>Includes bibliographical references (page 14).<br>A Monte Carlo algorithm for solving simple linear systems using a random walk is demonstrated and analyzed. The described algorithm solves for each element in the solution vector independently. Furthermore, it is demonstrated that this algorithm is easily parallelized. To reduce error, each processor can compute data for an independent element of the solution, or part of the data for a gi

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45

Zimmermann, Nils E. R., Timm J. Zabel, and Frerich J. Keil. "Transport into zeolite nanosheets: diffusion equations put to test." Diffusion fundamentals 20 (2013 ) 53, S. 1-2, 2013. https://ul.qucosa.de/id/qucosa%3A13629.

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46

Nadin, Grégoire. "Equations de réaction-diffusion et propagation en milieu hétérogène." Paris 6, 2008. http://www.theses.fr/2008PA066491.

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Cette thèse est consacrée à l'étude d'une équation de réaction-diffusion de type monostable en milieu hétérogène. Dans une première partie nous étudions les valeurs propres principales généralisées associées à une linéarisation de cette équation en milieu périodique en temps et en espace. Puis, nous donnons des propriétés d'existence et d'unicité des solutions entières de l'équation. Dans une seconde partie, nous prouvons l'existence de fronts pulsatoires en milieu périodique en temps et en espace. Une caractérisation de la vitesse de ces fronts est utilisée pour étudier la dépendance entre le

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47

Trojan, Alice von. "Finite difference methods for advection and diffusion." Title page, abstract and contents only, 2001. http://web4.library.adelaide.edu.au/theses/09PH/09phv948.pdf.

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Includes bibliographical references (leaves 158-163). Concerns the development of high-order finite-difference methods on a uniform rectangular grid for advection and diffuse problems with smooth variable coefficients. This technique has been successfully applied to variable-coefficient advection and diffusion problems. Demonstrates that the new schemes may readily be incorporated into multi-dimensional problems by using locally one-dimensional techniques, or that they may be used in process splitting algorithms to solve complicatef time-dependent partial differential equations.

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48

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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49

Manay, Siddharth. "Applications of anti-geometric diffusion of computer vision : thresholding, segmentation, and distance functions." Diss., Georgia Institute of Technology, 2003. http://hdl.handle.net/1853/33626.

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50

Carter, David, Boguslaw Kruczek, and F. Handan Tezel. "Application of Maxwell Stefan equations to characterize silicalite membranes." Diffusion fundamentals 24 (2015) 8, S. 1, 2015. https://ul.qucosa.de/id/qucosa%3A14522.

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