Relevant bibliographies by topics / Diffusion equations

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Diffusion equations'

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Published: 4 June 2021
Last updated: 21 February 2023

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Journal articles on the topic "Diffusion equations"

1

Slijepčević, Siniša. "Entropy of scalar reaction-diffusion equations." Mathematica Bohemica 139, no. 4 (2014): 597–605. http://dx.doi.org/10.21136/mb.2014.144137.

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Gomez, Francisco, Victor Morales, and Marco Taneco. "Analytical solution of the time fractional diffusion equation and fractional convection-diffusion equation." Revista Mexicana de Física 65, no. 1 (December 31, 2018): 82. http://dx.doi.org/10.31349/revmexfis.65.82.

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In this paper, we obtain analytical solutions for the time-fractional diffusion and time-fractional convection-diffusion equations. These equations are obtained from the standard equations by replacing the time derivative with a fractional derivative of order $\alpha$. Fractional operators of type Liouville-Caputo, Atangana-Baleanu-Caputo, fractional conformable derivative in Liouville-Caputo sense and Atangana-Koca-Caputo were used to model diffusion and convection-diffusion equation. The Laplace and Fourier transforms were applied to obtain the analytical solutions for the fractional order diffusion and convection-diffusion equations. The solutions obtained can be useful to understand the modeling of anomalous diffusive, subdiffusive systems and super-diffusive systems, transport processes, random walk and wave propagation phenomenon.
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Bögelein, Verena, Frank Duzaar, Paolo Marcellini, and Stefano Signoriello. "Nonlocal diffusion equations." Journal of Mathematical Analysis and Applications 432, no. 1 (December 2015): 398–428. http://dx.doi.org/10.1016/j.jmaa.2015.06.053.

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SOKOLOV, I. M., and A. V. CHECHKIN. "ANOMALOUS DIFFUSION AND GENERALIZED DIFFUSION EQUATIONS." Fluctuation and Noise Letters 05, no. 02 (June 2005): L275—L282. http://dx.doi.org/10.1142/s0219477505002653.

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Fractional diffusion equations are widely used to describe anomalous diffusion processes where the characteristic displacement scales as a power of time. The forms of such equations might differ with respect to the position of the corresponding fractional operator in addition to or instead of the whole-number derivative in the Fick's equation. For processes lacking simple scaling the corresponding description may be given by distributed-order equations. In the present paper different forms of distributed-order diffusion equations are considered. The properties of their solutions are discussed for a simple special case.
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Zubair, Muhammad. "Fractional diffusion equations and anomalous diffusion." Contemporary Physics 59, no. 4 (September 11, 2018): 406–7. http://dx.doi.org/10.1080/00107514.2018.1515252.

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Gurevich, Pavel, and Sergey Tikhomirov. "Systems of reaction-diffusion equations with spatially distributed hysteresis." Mathematica Bohemica 139, no. 2 (2014): 239–57. http://dx.doi.org/10.21136/mb.2014.143852.

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Fila, Marek, and Ján Filo. "Global behaviour of solutions to some nonlinear diffusion equations." Czechoslovak Mathematical Journal 40, no. 2 (1990): 226–38. http://dx.doi.org/10.21136/cmj.1990.102377.

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Abrashina-Zhadaeva, Natali. "A SPLITTING TYPE ALGORITHM FOR NUMERICAL SOLUTION OF PDES OF FRACTIONAL ORDER." Mathematical Modelling and Analysis 12, no. 4 (December 31, 2007): 399–408. http://dx.doi.org/10.3846/1392-6292.2007.12.399-408.

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Fractional order diffusion equations are generalizations of classical diffusion equations, treating super‐diffusive flow processes. In this paper, we examine a splitting type numerical methods to solve a class of two‐dimensional initial‐boundary value fractional diffusive equations. Stability, consistency and convergence of the methods are investigated. It is shown that both schemes are unconditionally stable. A numerical example is presented.
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Scheel, Arnd, and Erik S. Van Vleck. "Lattice differential equations embedded into reaction–diffusion systems." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 139, no. 1 (February 2009): 193–207. http://dx.doi.org/10.1017/s0308210507000248.

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We show that lattice dynamical systems naturally arise on infinite-dimensional invariant manifolds of reaction–diffusion equations with spatially periodic diffusive fluxes. The result connects wave-pinning phenomena in lattice differential equations and in reaction–diffusion equations in inhomogeneous media. The proof is based on a careful singular perturbation analysis of the linear part, where the infinite-dimensional manifold corresponds to an infinite-dimensional centre eigenspace.
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KOLTUNOVA, L. N. "ON AVERAGED DIFFUSION EQUATIONS." Chemical Engineering Communications 114, no. 1 (April 1992): 1–15. http://dx.doi.org/10.1080/00986449208936013.

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Dissertations / Theses on the topic "Diffusion equations"

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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 nous traitons l'équation dans le contexte de l'EDP non linéaire avec le flux singulier. Nous utilisons la théorie de gradient tangentiel pour caractériser l'équation d'état qui donne la relation entre le flux et le gradient de la solution. Dans le problème stationnaire, nous avons l'existence de la solution, nous avons également l'équivalence entre le problème minimisation initial, le problème dual et l'EDP. Dans l'équation de l'évolution, nous proposons l'existence, l'unicité de la solution. Le deuxième problème est régi par un opérateur discret. Nous étudions l'équation d'évolution discrète qui décrivent le processus d'effondrement du tas de sable. Ceci est un exemple typique de phénomènes auto-organisés critiques exposées par une slope critique. Nous considérons l'équation d'évolution discrète où la dynamique est régie par sous-gradient de la fonction d'indicateur de la boule unité. Nous commençons par établir le modèle, nous prouvons existence et l'unicité de la solution. Ensuite, en utilisant arguments de dualité nous étudions le calcul numérique de la solution et nous présentons quelques simulations numériques
This thesis is devoted to the study of evolution problems where the dynamic is governed by sub-gradient diffusion operator. We are interest in two kind of evolution problems. The first problem is governed by local operator of Leray-Lions type with a bounded domain. In this problem, the operator is maximal monotone and does not satisfied the standard polynomial growth control condition. Typical examples appears in the study of non-Neutonian fluid and also in the description of sub-gradient flows dynamics. To study the problem we handle the equation in the context of nonlinear PDE with singular flux. We use the theory of tangential gradient to characterize the state equation that gives the connection between the flux and the gradient of the solution. In the stationary problem, we have the existence of solution, we also get the equivalence between the initial minimization problem, the dual problem and the PDE. In the evolution one, we provide the existence, uniqueness of solution and the contractions. The second problem is governed by a discrete operator. We study the discrete evolution equation which describe the process of collapsing sandpile. This is a typical example of Self-organized critical phenomena exhibited by a critical slop. We consider the discrete evolution equation where the dynamic is governed by sub-gradient of indicator function of the unit ball. We begin by establish the model, we prove existence and uniqueness of the solution. Then by using dual arguments we study the numerical computation of the solution and we present some numerical simulations
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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, and we want to understand at which speed this invasion takes place. To answer this question, we set up a new method to study the speed of propagation when fractional diffusion is at stake and apply it on three different problems. Part I of the thesis is devoted to an analysis of the asymptotic location of the level sets of the solution to two different problems : Fisher-KPP models in periodic media and cooperative systems, both including fractional diffusion. On the first model, we prove that, under some assumptions on the periodic medium, the solution spreads exponentially fast in time and we find the precise exponent that appears in this exponential speed of propagation. We also carry out numerical simulations to investigate the dependence of the speed of propagation on the initial condition. On the second model, we prove that the speed of propagation is once again exponential in time, with an exponent depending on the smallest index of the fractional Laplacians at stake and on the reaction term. Part II of the thesis deals with a two dimensional environment, where reproduction of Fisher-KPP type and usual diffusion occur, except on a line of the plane, on which fractional diffusion takes place. The plane is referred to as 'the field' and the line to 'the road', as a reference to the biological situations we have in mind. Indeed, it has long been known that fast diffusion on roads can have a driving effect on the spread of epidemics. We prove that the speed of propagation is exponential in time on the road, whereas it depends linearly on time in the field. Contrary to the precise asymptotics obtained in Part I, for this model, we are not able to give a sharp location of the level sets on the road and in the field. The expansion shape of the level sets in the field is investigated through numerical simulations.
Esta tesis se centra en el comportamiento en tiempos grandes de las soluciones de la ecuación de Fisher- KPP de reacción-difusión con difusión fraccionaria. Este tipo de ecuación surge, por ejemplo, en la propagación espacial o en la propagación de especies biológicas (ratas, insectos,...). En la dinámica de poblaciones, la cantidad que se estudia representa la densidad de la población. Es conocido que, bajo algunas hipótesis específicas, la solución tiende a un estado estable del problema de evolución, cuando el tiempo tiende a infinito. En otras palabras, la población invade el medio, lo que corresponde a la supervivencia de la especie, y nosotros queremos entender con qué velocidad se lleva a cabo esta invasión. Para responder a esta pregunta, hemos creado un nuevo método para estudiar la velocidad de propagación cuando se consideran difusiones fraccionarias, además hemos aplicado este método en tres problemas diferentes. La Parte I de la tesis está dedicada al análisis de la ubicación asintótica de los conjuntos de nivel de la solución de dos problemas diferentes: modelos de Fisher- KPP en medios periódicos y sistemas cooperativos, ambos consideran difusión fraccionaria. En el primer modelo, se prueba que, bajo ciertas hipótesis sobre el medio periódico, la solución se propaga exponencialmente rápido en el tiempo, además encontramos el exponente exacto que aparece en esta velocidad de propagación exponencial. También llevamos a cabo simulaciones numéricas para investigar la dependencia de la velocidad de propagación con la condición inicial. En el segundo modelo, se prueba que la velocidad de propagación es nuevamente exponencial en el tiempo, con un exponente que depende del índice más pequeño de los Laplacianos fraccionarios y también del término de reacción. La Parte II de la tesis ocurre en un entorno de dos dimensiones, donde se reproduce un tipo ecuación de Fisher- KPP con difusión estándar, excepto en una línea del plano, en el que la difusión fraccionada aparece. El plano será llamado "campo" y la línea "camino", como una referencia a las situaciones biológicas que tenemos en mente. De hecho, desde hace tiempo se sabe que la difusión rápida en los caminos puede causar un efecto en la propagación de epidemias. Probamos que la velocidad de propagación es exponencial en el tiempo en el camino, mientras que depende linealmente del tiempo en el campo. Contrariamente a los precisos exponentes obtenidos en la Parte I, para este modelo, no fuimos capaces de dar una localización exacta de los conjuntos de nivel en la carretera y en el campo. La forma de propagación de los conjuntos de nivel en el campo se investiga a través de simulaciones numéricas
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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 Mastergleichung zur Berechnung der Zeitentwicklung der Wahrscheinlichkeitsverteilung. Zur Charakterisierung der Diffusion auf regelmäßigen und zufälligen Teppichen bestimmen wir die Abfallzeit der Wahrscheinlichkeitsverteilung, die mittlere Austrittszeit und die Random Walk Dimension. Somit können wir den Einfluss zufälliger Strukturen auf die Diffusion aufzeigen. Superdiffusive Prozesse werden im zweiten Teil der Arbeit mit Hilfe der Diffusionsgleichung untersucht. Deren zweite Ableitung im Ort erweitern wir auf nichtganzzahlige Ordnungen, um die fraktalen Eigenschaften der Umgebung darzustellen. Die resultierende raum-fraktionale Diffusionsgleichung spannt ein Übergangsregime von der irreversiblen Diffusionsgleichung zur reversiblen Wellengleichung auf. Deren Lösungen untersuchen wir mittels verschiedener Entropien, wie Shannon, Tsallis oder Rényi Entropien, und deren Entropieproduktionsraten, welche natürliche Maße für die Irreversibilität sind. Das dabei gefundene Entropieproduktions-Paradoxon, d. h. ein unerwarteter Anstieg der Entropieproduktionsrate bei sinkender Irreversibilität des Prozesses, können wir nach geeigneter Reskalierung der Entropien auflösen
The aim of this thesis is the examination of sub- and superdiffusive processes in fractal structures. The focus of the work concentrates on two separate approaches that are chosen and varied according to the corresponding regime. Thus, we obtain new insights about the underlying mechanisms and a more appropriate way of description for both regimes. In the first part subdiffusion is considered, which plays a crucial role for transport processes, as in living tissues. First, we model the fractal state space via finite Sierpinski carpets with absorbing boundary conditions and we solve the master equation to compute the time development of the probability distribution. To characterize the diffusion on regular as well as random carpets we determine the longest decay time of the probability distribution, the mean exit time and the Random walk dimension. Thus, we can verify the influence of random structures on the diffusive dynamics. In the second part of this thesis superdiffusive processes are studied by means of the diffusion equation. Its second order space derivative is extended to fractional order, which represents the fractal properties of the surrounding media. The resulting space-fractional diffusion equations span a linking regime from the irreversible diffusion equation to the reversible (half) wave equation. The corresponding solutions are analyzed by different entropies, as the Shannon, Tsallis or Rényi entropies and their entropy production rates, which are natural measures of irreversibility. We find an entropy production paradox, i. e. an unexpected increase of the entropy production rate by decreasing irreversibility of the processes. Due to an appropriate rescaling of the entropy we are able to resolve the paradox
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Fei, Ning Fei. "Studies in reaction-diffusion equations." Thesis, Heriot-Watt University, 2003. http://hdl.handle.net/10399/310.

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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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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.
Kyoto Journal of Mathematics, vol35(3), pp.539-567, 1995, http://projecteuclid.org/euclid.kjm/1250518709
Kyoto University (京都大学)
0048
新制・課程博士
博士(理学)
甲第5884号
理博第1591号
新制||理||889(附属図書館)
UT51-95-D203
京都大学大学院工学研究科数学専攻
(主査)教授 西田 孝明, 教授 渡辺 信三, 教授 岩崎 敷久
学位規則第4条第1項該当
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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 comprenant une diffusion fractionnaire : un modèle de type Fisher-KPP en milieu périodique et un système coopératif. Dans les deux cas, nous montrons, sous certaines conditions, que la vitesse de propagation est exponentielle en temps, et nous donnons une expression précise de l'exposant de propagation. Nous menons des simulations numériques pour étudier la dépendance de cette vitesse de propagation en la donnée initiale. Dans une seconde partie, nous traitons un environnement bidimensionnel, dans lequel le terme de reproduction est de type Fisher-KPP et le terme diffusif est donné par un laplacien standard, excepté sur une ligne du plan où une diffusion fractionnaire intervient. Le plan est nommé "le champ" et la ligne "la route", en référence aux situations biologiques que nous voulons modéliser. Nous prouvons que la vitesse de propagation est exponentielle en temps sur la route, alors qu'elle dépend linéairement du temps dans le champ. La forme des lignes de niveau dans le champ est étudiée au travers de simulations numériques
This thesis focuses on the long time behaviour, and more precisely on fast propagation, in Fisher-KPP reaction diffusion equations involving fractional diffusion. This type of equation arises, for example, in spreading of biological species. Under some specific assumptions, the population invades the medium and we want to understand at which speed this invasion takes place when fractional diffusion is at stake. To answer this question, we set up a new method and apply it on different models. In a first part, we study two different problems, both including fractional diffusion : Fisher-KPP models in periodic media and cooperative systems. In both cases, we prove, under additional assumptions, that the solution spreads exponentially fast in time and we find the precise exponent of propagation. We also carry out numerical simulations to investigate the dependence of the speed of propagation on the initial condition. In a second part, we deal with a two dimensional environment, where reproduction of Fisher-KPP type and usual diffusion occur, except on a line of the plane, on which fractional diffusion takes place. The plane is referred to as "the field" and the line to "the road", as a reference to the biological situations we have in mind. We prove that the speed of propagation is exponential in time on the road, whereas it depends linearly on time in the field. The expansion shape of the level sets in the field is investigated through numerical simulations
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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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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 approximation des équations sur des semi-intervales infinis $(-r,+\infty)$. L'unicité et la monotonie des solutions sont quand elles obtenues par méthode de glissement. Le comportement asymptotique ainsi que des formules pour les vitesses sont aussi établis.
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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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Books on the topic "Diffusion equations"

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Seizō, Itō. Diffusion equations. Providence, R.I: American Mathematical Society, 1992.

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Favini, Angelo. Degenerate Nonlinear Diffusion Equations. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012.

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Favini, Angelo, and Gabriela Marinoschi. Degenerate Nonlinear Diffusion Equations. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-28285-0.

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Masao, Nagasawa. Schrödinger equations and diffusion theory. Basel: Birkhäuser Verlag, 1993.

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Nagasawa, Masao. Schrödinger Equations and Diffusion Theory. Basel: Springer Basel, 1993. http://dx.doi.org/10.1007/978-3-0348-0560-5.

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Nagasawa, Masao. Schrödinger Equations and Diffusion Theory. Basel: Birkhäuser Basel, 1993. http://dx.doi.org/10.1007/978-3-0348-8568-3.

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Lam, King-Yeung, and Yuan Lou. Introduction to Reaction-Diffusion Equations. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-20422-7.

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Nonlocal diffusion problems. Providence, R.I: American Mathematical Society, 2010.

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1955-, Caristi Gabriella, and Mitidieri Enzo, eds. Reaction diffusion systems. New York: Marcel Dekker, 1998.

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Shock waves and reaction-diffusion equations. 2nd ed. New York: Springer-Verlag, 1994.

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Book chapters on the topic "Diffusion equations"

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Linge, Svein, and Hans Petter Langtangen. "Diffusion Equations." In Finite Difference Computing with PDEs, 207–322. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-55456-3_3.

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Shewmon, Paul. "Diffusion Equations." In Diffusion in Solids, 9–51. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-48206-4_1.

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Itô, Seizô. "Diffusion Equations." In Kôsaku Yosida Collected Papers, 421–87. Tokyo: Springer Japan, 1992. http://dx.doi.org/10.1007/978-4-431-65859-7_6.

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Kavdia, Mahendra. "Parabolic Differential Equations, Diffusion Equation." In Encyclopedia of Systems Biology, 1621–24. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4419-9863-7_273.

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Stroock, Daniel W., and S. R. Srinivasa Varadhan. "Stochastic Differential Equations." In Multidimensional Diffusion Processes, 122–35. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/3-540-28999-2_6.

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Eidelman, Samuil D., Anatoly N. Kochubei, and Stepan D. Ivasyshen. "Fractional Diffusion Equations." In Analytic Methods in the Theory of Differential and Pseudo-Differential Equations of Parabolic Type, 321–61. Basel: Birkhäuser Basel, 2004. http://dx.doi.org/10.1007/978-3-0348-7844-9_5.

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Jüngel, Ansgar. "Drift-Diffusion Equations." In Transport Equations for Semiconductors, 1–29. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-540-89526-8_5.

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Mei, Zhen. "Reaction-Diffusion Equations." In Numerical Bifurcation Analysis for Reaction-Diffusion Equations, 1–6. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/978-3-662-04177-2_1.

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Da Prato, Giuseppe. "Reaction-Diffusion Equations." In Kolmogorov Equations for Stochastic PDEs, 99–130. Basel: Birkhäuser Basel, 2004. http://dx.doi.org/10.1007/978-3-0348-7909-5_4.

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Woyczynski, Wojbor A. "Nonlinear Diffusion Equations." In Diffusion Processes, Jump Processes, and Stochastic Differential Equations, 107–14. Boca Raton: Chapman and Hall/CRC, 2022. http://dx.doi.org/10.1201/9781003216759-9.

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Conference papers on the topic "Diffusion equations"

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Hassanpour, H., E. Nadernejad, and H. Miar. "Image enhancement using diffusion equations." In 2007 9th International Symposium on Signal Processing and Its Applications (ISSPA). IEEE, 2007. http://dx.doi.org/10.1109/isspa.2007.4555608.

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Popescu, Emil, Cristiana Dumitrache, Vasile Mioc, and Nedelia A. Popescu. "Fractional diffusion equations and applications." In Flows, Boundaries, Interactions. AIP, 2007. http://dx.doi.org/10.1063/1.2790342.

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Hanyga, Andrzej. "Fractional diffusion and wave equations." In Mathematical Models and Methods for Smart Materials. WORLD SCIENTIFIC, 2002. http://dx.doi.org/10.1142/9789812776273_0017.

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Quintana Murillo, Joaqui´n, and Santos Bravo Yuste. "On an Explicit Difference Method for Fractional Diffusion and Diffusion-Wave Equations." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-86625.

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Abstract:
An explicit difference scheme for solving fractional diffusion and fractional diffusion-wave equations, in which the fractional derivative is in the Caputo form, is considered. The two equations are studied separately: for the fractional diffusion equation, the L1 discretization formula is employed, whereas the L2 discretization formula is used for the fractional diffusion-wave equation. Its accuracy is similar to other well-known explicit difference schemes, but its region of stability is larger. The stability analysis is carried out by means of a procedure similar to the standard von Neumann method. The stability bound, which is given in terms of the the Riemann Zeta function, is checked numerically.
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SALVARANI, F., and J. L. VÁZQUEZ. "FROM KINETIC SYSTEMS TO DIFFUSION EQUATIONS." In Proceedings of the 12th Conference on WASCOM 2003. WORLD SCIENTIFIC, 2004. http://dx.doi.org/10.1142/9789812702937_0055.

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Hwang, Jeehyun, Jeongwhan Choi, Hwangyong Choi, Kookjin Lee, Dongeun Lee, and Noseong Park. "Climate Modeling with Neural Diffusion Equations." In 2021 IEEE International Conference on Data Mining (ICDM). IEEE, 2021. http://dx.doi.org/10.1109/icdm51629.2021.00033.

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Koprucki, Thomas, and Klaus Gartner. "Discretization scheme for drift-diffusion equations with strong diffusion enhancement." In 2012 12th International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD). IEEE, 2012. http://dx.doi.org/10.1109/nusod.2012.6316560.

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ISHII, HITOSHI, and HIROYOSHI MITAKE. "TWO REMARKS ON PERIODIC SOLUTIONS OF HAMILTON-JACOBI EQUATIONS." In The International Conference on Reaction-Diffusion System and Viscosity Solutions. WORLD SCIENTIFIC, 2009. http://dx.doi.org/10.1142/9789812834744_0005.

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GEORGI, M., and N. JANGLE. "SPIRAL WAVE MOTION IN REACTION-DIFFUSION SYSTEMS." In Proceedings of the International Conference on Differential Equations. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812702067_0108.

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Poláčik, P. "SYMMETRY PROPERTIES OF POSITIVE SOLUTIONS OF PARABOLIC EQUATIONS: A SURVEY." In The International Conference on Reaction-Diffusion System and Viscosity Solutions. WORLD SCIENTIFIC, 2009. http://dx.doi.org/10.1142/9789812834744_0009.

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Reports on the topic "Diffusion equations"

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Wang, Chi-Jen. Analysis of discrete reaction-diffusion equations for autocatalysis and continuum diffusion equations for transport. Office of Scientific and Technical Information (OSTI), January 2013. http://dx.doi.org/10.2172/1226552.

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Kallianput, G., I. Mitoma, and R. L. Wolpert. Diffusion Equations in Duals of Nuclear Spaces. Fort Belvoir, VA: Defense Technical Information Center, July 1988. http://dx.doi.org/10.21236/ada200078.

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Fujisaki, Masatoshi. Normed Bellman Equation with Degenerate Diffusion Coefficients and Its Application to Differential Equations. Fort Belvoir, VA: Defense Technical Information Center, October 1987. http://dx.doi.org/10.21236/ada190319.

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Hale, Jack K., and Kunimochi Sakamoto. Shadow Systems and Attractors in Reaction-Diffusion Equations,. Fort Belvoir, VA: Defense Technical Information Center, April 1987. http://dx.doi.org/10.21236/ada185804.

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Wenocur, Michael L. Diffusion First Passage Times: Approximations and Related Differential Equations,. Fort Belvoir, VA: Defense Technical Information Center, January 1986. http://dx.doi.org/10.21236/ada185592.

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Fields, Mary A. Modeling Large Scale Troop Movement Using Reaction Diffusion Equations. Fort Belvoir, VA: Defense Technical Information Center, September 1993. http://dx.doi.org/10.21236/ada270701.

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Heineike, Benjamin M. Modeling Morphogenesis with Reaction-Diffusion Equations Using Galerkin Spectral Methods. Fort Belvoir, VA: Defense Technical Information Center, May 2002. http://dx.doi.org/10.21236/ada403766.

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Ahmed, Hoda F. Gegenbauer Collocation Algorithm for Solving Twodimensional Time-space Fractional Diffusion Equations. "Prof. Marin Drinov" Publishing House of Bulgarian Academy of Sciences, August 2019. http://dx.doi.org/10.7546/crabs.2019.08.04.

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Knapp, Charles E., and Charles W. Cranfill. Comparison of Numeric to Analytic Solutions for a Class of Nonlinear Diffusion Equations. Office of Scientific and Technical Information (OSTI), October 1992. http://dx.doi.org/10.2172/1193616.

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Ahmed, Hoda F. Analytic Approximate Solutions for the 1D and 2D Nonlinear Fractional Diffusion Equations of Fisher Type. "Prof. Marin Drinov" Publishing House of Bulgarian Academy of Sciences, March 2020. http://dx.doi.org/10.7546/crabs.2020.03.04.

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