Front Tracking para sistemas hiperbólicos de leyes de conservación
ilustraciones, diagramas, figuras
- Autores:
-
Castillo Barajas, Jonhatan
- Tipo de recurso:
- Fecha de publicación:
- 2023
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/85436
- Palabra clave:
- 510 - Matemáticas
510 - Matemáticas::515 - Análisis
Leyes de la conservación (Física)
Cauchy-Riemann, Ecuaciones de
Entropía
Conservation laws (Physics)
Cauchy-Riemann equations
Entropy
Leyes de conservación
Problema de Riemann
Condición de entropía
Variación acotada
Front tracking
Conservation laws
Riemann problem
Entropy condition
Bounded variation
Función de variación acotada
Function of bounded variation
- Rights
- openAccess
- License
- Atribución-NoComercial 4.0 Internacional
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| dc.title.spa.fl_str_mv |
Front Tracking para sistemas hiperbólicos de leyes de conservación |
| dc.title.translated.eng.fl_str_mv |
Front Tracking for hyperbolic conservation laws systems |
| title |
Front Tracking para sistemas hiperbólicos de leyes de conservación |
| spellingShingle |
Front Tracking para sistemas hiperbólicos de leyes de conservación 510 - Matemáticas 510 - Matemáticas::515 - Análisis Leyes de la conservación (Física) Cauchy-Riemann, Ecuaciones de Entropía Conservation laws (Physics) Cauchy-Riemann equations Entropy Leyes de conservación Problema de Riemann Condición de entropía Variación acotada Front tracking Conservation laws Riemann problem Entropy condition Bounded variation Función de variación acotada Function of bounded variation |
| title_short |
Front Tracking para sistemas hiperbólicos de leyes de conservación |
| title_full |
Front Tracking para sistemas hiperbólicos de leyes de conservación |
| title_fullStr |
Front Tracking para sistemas hiperbólicos de leyes de conservación |
| title_full_unstemmed |
Front Tracking para sistemas hiperbólicos de leyes de conservación |
| title_sort |
Front Tracking para sistemas hiperbólicos de leyes de conservación |
| dc.creator.fl_str_mv |
Castillo Barajas, Jonhatan |
| dc.contributor.advisor.none.fl_str_mv |
Rendón Arbeláez, Leonardo |
| dc.contributor.author.none.fl_str_mv |
Castillo Barajas, Jonhatan |
| dc.subject.ddc.spa.fl_str_mv |
510 - Matemáticas 510 - Matemáticas::515 - Análisis |
| topic |
510 - Matemáticas 510 - Matemáticas::515 - Análisis Leyes de la conservación (Física) Cauchy-Riemann, Ecuaciones de Entropía Conservation laws (Physics) Cauchy-Riemann equations Entropy Leyes de conservación Problema de Riemann Condición de entropía Variación acotada Front tracking Conservation laws Riemann problem Entropy condition Bounded variation Función de variación acotada Function of bounded variation |
| dc.subject.lcc.spa.fl_str_mv |
Leyes de la conservación (Física) Cauchy-Riemann, Ecuaciones de Entropía |
| dc.subject.lcc.eng.fl_str_mv |
Conservation laws (Physics) Cauchy-Riemann equations Entropy |
| dc.subject.proposal.spa.fl_str_mv |
Leyes de conservación Problema de Riemann Condición de entropía Variación acotada |
| dc.subject.proposal.eng.fl_str_mv |
Front tracking Conservation laws Riemann problem Entropy condition Bounded variation |
| dc.subject.wikidata.spa.fl_str_mv |
Función de variación acotada |
| dc.subject.wikidata.eng.fl_str_mv |
Function of bounded variation |
| description |
ilustraciones, diagramas, figuras |
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2023 |
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2023 |
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2024-01-24T22:21:17Z |
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2024-01-24T22:21:17Z |
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Trabajo de grado - Maestría |
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info:eu-repo/semantics/masterThesis |
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info:eu-repo/semantics/acceptedVersion |
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Text |
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Universidad Nacional de Colombia |
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https://repositorio.unal.edu.co/ |
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Universidad Nacional de Colombia Repositorio Institucional Universidad Nacional de Colombia |
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spa |
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BAITI,P; JENSSEN, H. K. On the front-tracking algorithm. Journal of mathematical analysis and applications 217 (1998), Nr 2, p. 295-404. Bateman, H.: Some recent researches on the motion of fluids. En: Monthly Weather Review 43 (1915), Nr. 4, p. 163–170 Bressan, A.: Global solutions of systems of conservation laws by wave-front tracking. En: Journal of mathematical analysis and applications 170 (1992), Nr. 2, p. 414–432 Bressan, A.: The unique limit of the Glimm scheme. En: Archive for rational mechanics and analysis 130 (1995), p. 205–230 Bressan, A. ; Goatin, P.: Oleinik type estimates and uniqueness for n× n conservation laws. En: Journal of differential equations 156 (1999), Nr. 1, p. 26–49 Bressan, A. ; LeFloch, P.: Uniqueness of weak solutions to systems of conservation laws. En: Archive for Rational Mechanics and Analysis 140 (1997), Nr. 4, p. 301–317 Bressan, A. ; Lewicka, M.: A uniqueness condition for hyperbolic systems of conservation laws. En: Discrete and Continuous Dynamical Systems 6 (2000), Nr. 3, p. 673–682 Bressan, A. ; Liu, T. ; Yang, T.: L1 stability estimates for n× n conservation laws. En: Archive for rational mechanics and analysis 149 (1999), Nr. 1, p. 1–22 Buckley, S. E. ; Leverett, M. C.: Mechanism of fluid displacement in sands. En: Transactions of the AIME 146 (1942), Nr. 01, p. 107–116 Bunt, L. N. H.: Bijdrage tot de theorie der convexe puntverzamelingen. Rijksuniversiteitte Groningen, 1934 Burgers, J. M.: A mathematical model illustrating the theory of turbulence. En: Advances in applied mechanics 1 (1948), p. 171–199 Chorin, A. J. ; Marsden, J. E.: A mathematical introduction to fluid mechanics. Vol. 3. Springer Science & Business Media, 1990 Crandall, M. G. ; Tartar, L.: Some relations between nonexpansive and order preserving mappings. En: Proceedings of the American Mathematical Society 78 (1980), Nr. 3, p. 385–390 Dafermos, C. M.: Polygonal approximations of solutions of the initial value problem for a conservation law. En: Journal of mathematical analysis and applications 38 (1972), Nr. 1, p. 33–41 DiPerna, R. J.: Global existence of solutions to nonlinear hyperbolic systems of conservation laws. (1976) Evans, L. C. ; Gariepy, R. F.: Measure Theory and Fine Properties of Functions. Vol. 5. CRC Press, 1991 Fenchel, W.: Über krümmung und windung geschlossener raumkurven. En: Mathematische Annalen 101 (1929), Nr. 1, p. 238–252 Gel’fand, I.: Some questions in the theory of quasilinear equations. En: Uspehi Mat. Nuuk 14 (1959), p. 87–158 Glimm, J.: Solutions in the large for nonlinear hyperbolic systems of equations. En: Communications on pure and applied mathematics 18 (1965), Nr. 4, p. 697–715 Hanche-Olsen, H. ; Holden, H.: The Kolmogorov–Riesz compactness theorem. En: Expositiones Mathematicae (2010), Nr. 4, p. 385–394 Hanner, O. ; Rådström, H.: A generalization of a theorem of Fenchel. En: Proceedings of the American Mathematical Society 2 (1951), Nr. 4, p. 589–593 Holden, H. ; Holden, L. ; Høegh-Krohn, R.: A numerical method for first order nonlinear scalar conservation laws in one-dimension. En: Computers & Mathematics with Applications 15 (1988), Nr. 6-8, p. 595–602 Holden, H. ; Risebro, N. H.: Front Tracking for Hyperbolic Conservation Laws. Vol. 152. Springer Science & Business Media, 2007 Hopf, E.: The partial differential equation ut + uux = μuxx. En: Communications on Pure and Applied Mathematics (1950), Nr. 3, p. 201–230 Hugoniot, H.: Sur un théorème général relatif à la propagation du mouvement dans les corps. En: Comptes Rendus des Séances de lÁcadémie des Sciences (1886), p. 858–860 Kesavan, S.: Topics in Functional Analysis and Applications. New Age International, 2008 Kružkov, S. N.: First order quasilinear equations in several independent variables. En: Mathematics of the USSR-Sbornik (1970), Nr. 2, p. 217 Langseth, J. O.: On an implementation of a front tracking method for hyperbolic conservation laws. En: Advances in engineering software 26 (1996), Nr. 1, p. 45–63 Langseth, J. O. ; Risebro, N. H. ; Tveito, A.: A conservative front tracking scheme for 1D hyperbolic conservation laws. En: Nonlinear Hyperbolic Problems: Theoretical, Applied, and Computational Aspects: Proceedings of the Fourth International Conference on Hyperbolic Problems, Taormina, Italy, April 3 to 8, 1992 Springer, 1993, p. 385–392 Lax, P. D.: Hyperbolic systems of conservation laws II. En: Communications on Pure and Applied Mathematics (1957), Nr. 4, p. 537–566 Lax, P. D.: Hyperbolic systems of conservation laws in several space variables / New York Univ., NY (USA). Courant Mathematics and Computing Lab. 1985. – Informe de Investigación LeVeque, R.: Numerical methods for conservation laws. Vol. 214. Springer, 1992 Limaye, B.: Functional Analysis. New Age International (P) Limited, Publishers, 1997 Lucier, B. J.: A moving mesh numerical method for hyperbolic conservation laws. En: Mathematics of computation 46 (1986), Nr. 173, p. 59–69 Meise, R. ; Vogt, D.: Introduction to functional analysis. Clarendon Press, 1997 Munkres, J. R.: Topology. Pearson Education, 2019 Oleînik, O. A.: Discontinuous solutions of non-linear differential equations. En: Uspekhi Matematicheskikh Nauk (1957), Nr. 3, p. 3–73 Rankine, W. J. M.: On the Thermodynamic Theory of Waves of Finite Longitudinal Disturbances. En: Philosophical Transactions of the Royal Society (1870), p. 277–288 Riemann, B.: Über die Fortpflanzung ebener Luftwellen von endlicher Schwingungsweite. En: Göttinger Nachrichten (1860), p. 192–197 Risebro, N. H.: A front-tracking alternative to the random choice method. En: Proceedings of the American Mathematical Society 117 (1993), Nr. 4, p. 1125–1139 Rudin, W.: Functional Analysis. MacGraw-Hill Science, 1991 Schatzman, M.: Continuous Glimm functionals and uniqueness of solutions of the Riemann problem. En: Indiana University Mathematics Journal 34 (1985), Nr. 3, p. 533–589 Sherwood, T. K. ; Pigford, R. L. ; Wilke, C. R.: Mass Transfer. Mac Graw-Hill, Chemical Engineering Series, 1975 Smoller, J.: Shock waves and reaction-diffusion equations. Vol. 258. Springer Science & Business Media, 2012 Webster, R.: Convexity. Oxford University Press, 1994 Whittaker, E. T. ; Watson, G. N.: A Course of Modern Analysis: an Introduction to the General Theory of Infinite Processes and of Analytic Functions; with an Account of the Principal Transcendental Functions. Cambridge University Press, 1928 Yartsev, A.: Diffusion of gases through the alveolar membrane. Deranged Physiology, https://derangedphysiology.com/main/cicm-primary-exam/required-reading/respiratory-system, 2020 |
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Atribución-NoComercial 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Rendón Arbeláez, Leonardoe1b98bb70cc48eb2f570f8cffd6f7b9fCastillo Barajas, Jonhatana1b4ec230204a5673c0f97fb0eb5276b2024-01-24T22:21:17Z2024-01-24T22:21:17Z2023https://repositorio.unal.edu.co/handle/unal/85436Universidad Nacional de ColombiaRepositorio Institucional Universidad Nacional de Colombiahttps://repositorio.unal.edu.co/ilustraciones, diagramas, figurasEn este documento se estudia el método de aproximación de soluciones de leyes de conservación conocido como \textit{front tracking}, considerando el caso escalar y el caso de sistemas hiperbólicos. En ambos casos, se estudian las soluciones del problema de Riemann \begin{equation*} u_t+f(u)_x=0,\quad u(x,0)=\begin{cases} u_l, &x<0,\\ u_r, &x\geq 0, \end{cases} \end{equation*} con $(x,t)\in \R\times [0,\infty)$, considerando algunas condiciones de entropía. Este problema es crucial para introducir el método de front tracking, el cual consiste en analizar las discontinuidades del problema de Cauchy con una condición inicial aproximada por funciones constantes a trozos, resolver las interacciones entre las discontinuidades y funciona como método numérico para aproximar las soluciones de este problema. Además, se estudian las propiedades de las soluciones del problema de Cauchy que se obtienen como límite de soluciones construidas mediante front tracking. (Texto tomado de la fuente)In this paper we study the approximation method of solutions of conservation laws known as \textit{front tracking}, considering the scalar case and the case of hyperbolic systems. In both cases, we study the solutions of the Riemann problem \begin{equation*} u_t+f(u)_x=0,\quad u(x,0)=\begin{cases} u_l, &x<0,\\ u_r, &x \geq 0, \end{cases} \end{equation*} with $(x,t)\in \mathbb{R} \times [0,\infty)$, considering some entropy conditions. This problem is crucial to introduce the front tracking method, which consists of analyzing the discontinuities of the Cauchy problem with an initial condition approximated by piecewise constant functions, solving the interactions between the discontinuities and works as a numerical method to approximate the solutions of this problem. In addition, the properties of the solutions of the Cauchy problem obtained as limits of solutions constructed by front tracking are studied.MaestríaMagíster en Ciencias - Matemáticasxi, 128 páginasapplication/pdfspaUniversidad Nacional de ColombiaBogotá - Ciencias - Maestría en Ciencias - MatemáticasFacultad de CienciasBogotá, ColombiaUniversidad Nacional de Colombia - Sede Bogotá510 - Matemáticas510 - Matemáticas::515 - AnálisisLeyes de la conservación (Física)Cauchy-Riemann, Ecuaciones deEntropíaConservation laws (Physics)Cauchy-Riemann equationsEntropyLeyes de conservaciónProblema de RiemannCondición de entropíaVariación acotadaFront trackingConservation lawsRiemann problemEntropy conditionBounded variationFunción de variación acotadaFunction of bounded variationFront Tracking para sistemas hiperbólicos de leyes de conservaciónFront Tracking for hyperbolic conservation laws systemsTrabajo de grado - Maestríainfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/acceptedVersionTexthttp://purl.org/redcol/resource_type/TMBAITI,P; JENSSEN, H. K. On the front-tracking algorithm. Journal of mathematical analysis and applications 217 (1998), Nr 2, p. 295-404.Bateman, H.: Some recent researches on the motion of fluids. En: Monthly Weather Review 43 (1915), Nr. 4, p. 163–170Bressan, A.: Global solutions of systems of conservation laws by wave-front tracking. En: Journal of mathematical analysis and applications 170 (1992), Nr. 2, p. 414–432Bressan, A.: The unique limit of the Glimm scheme. En: Archive for rational mechanics and analysis 130 (1995), p. 205–230Bressan, A. ; Goatin, P.: Oleinik type estimates and uniqueness for n× n conservation laws. En: Journal of differential equations 156 (1999), Nr. 1, p. 26–49Bressan, A. ; LeFloch, P.: Uniqueness of weak solutions to systems of conservation laws. En: Archive for Rational Mechanics and Analysis 140 (1997), Nr. 4, p. 301–317Bressan, A. ; Lewicka, M.: A uniqueness condition for hyperbolic systems of conservation laws. En: Discrete and Continuous Dynamical Systems 6 (2000), Nr. 3, p. 673–682Bressan, A. ; Liu, T. ; Yang, T.: L1 stability estimates for n× n conservation laws. En: Archive for rational mechanics and analysis 149 (1999), Nr. 1, p. 1–22Buckley, S. E. ; Leverett, M. C.: Mechanism of fluid displacement in sands. En: Transactions of the AIME 146 (1942), Nr. 01, p. 107–116Bunt, L. N. H.: Bijdrage tot de theorie der convexe puntverzamelingen. Rijksuniversiteitte Groningen, 1934Burgers, J. M.: A mathematical model illustrating the theory of turbulence. En: Advances in applied mechanics 1 (1948), p. 171–199Chorin, A. J. ; Marsden, J. E.: A mathematical introduction to fluid mechanics. Vol. 3. Springer Science & Business Media, 1990Crandall, M. G. ; Tartar, L.: Some relations between nonexpansive and order preserving mappings. En: Proceedings of the American Mathematical Society 78 (1980), Nr. 3, p. 385–390Dafermos, C. M.: Polygonal approximations of solutions of the initial value problem for a conservation law. En: Journal of mathematical analysis and applications 38 (1972), Nr. 1, p. 33–41DiPerna, R. J.: Global existence of solutions to nonlinear hyperbolic systems of conservation laws. (1976)Evans, L. C. ; Gariepy, R. F.: Measure Theory and Fine Properties of Functions. Vol. 5. CRC Press, 1991Fenchel, W.: Über krümmung und windung geschlossener raumkurven. En: Mathematische Annalen 101 (1929), Nr. 1, p. 238–252Gel’fand, I.: Some questions in the theory of quasilinear equations. En: Uspehi Mat. Nuuk 14 (1959), p. 87–158Glimm, J.: Solutions in the large for nonlinear hyperbolic systems of equations. En: Communications on pure and applied mathematics 18 (1965), Nr. 4, p. 697–715Hanche-Olsen, H. ; Holden, H.: The Kolmogorov–Riesz compactness theorem. En: Expositiones Mathematicae (2010), Nr. 4, p. 385–394Hanner, O. ; Rådström, H.: A generalization of a theorem of Fenchel. En: Proceedings of the American Mathematical Society 2 (1951), Nr. 4, p. 589–593Holden, H. ; Holden, L. ; Høegh-Krohn, R.: A numerical method for first order nonlinear scalar conservation laws in one-dimension. En: Computers & Mathematics with Applications 15 (1988), Nr. 6-8, p. 595–602Holden, H. ; Risebro, N. H.: Front Tracking for Hyperbolic Conservation Laws. Vol. 152. Springer Science & Business Media, 2007Hopf, E.: The partial differential equation ut + uux = μuxx. En: Communications on Pure and Applied Mathematics (1950), Nr. 3, p. 201–230Hugoniot, H.: Sur un théorème général relatif à la propagation du mouvement dans les corps. En: Comptes Rendus des Séances de lÁcadémie des Sciences (1886), p. 858–860Kesavan, S.: Topics in Functional Analysis and Applications. New Age International, 2008Kružkov, S. N.: First order quasilinear equations in several independent variables. En: Mathematics of the USSR-Sbornik (1970), Nr. 2, p. 217Langseth, J. O.: On an implementation of a front tracking method for hyperbolic conservation laws. En: Advances in engineering software 26 (1996), Nr. 1, p. 45–63Langseth, J. O. ; Risebro, N. H. ; Tveito, A.: A conservative front tracking scheme for 1D hyperbolic conservation laws. En: Nonlinear Hyperbolic Problems: Theoretical, Applied, and Computational Aspects: Proceedings of the Fourth International Conference on Hyperbolic Problems, Taormina, Italy, April 3 to 8, 1992 Springer, 1993, p. 385–392Lax, P. D.: Hyperbolic systems of conservation laws II. En: Communications on Pure and Applied Mathematics (1957), Nr. 4, p. 537–566Lax, P. D.: Hyperbolic systems of conservation laws in several space variables / New York Univ., NY (USA). Courant Mathematics and Computing Lab. 1985. – Informe de InvestigaciónLeVeque, R.: Numerical methods for conservation laws. Vol. 214. Springer, 1992Limaye, B.: Functional Analysis. New Age International (P) Limited, Publishers, 1997Lucier, B. J.: A moving mesh numerical method for hyperbolic conservation laws. En: Mathematics of computation 46 (1986), Nr. 173, p. 59–69Meise, R. ; Vogt, D.: Introduction to functional analysis. Clarendon Press, 1997Munkres, J. R.: Topology. Pearson Education, 2019Oleînik, O. A.: Discontinuous solutions of non-linear differential equations. En: Uspekhi Matematicheskikh Nauk (1957), Nr. 3, p. 3–73Rankine, W. J. M.: On the Thermodynamic Theory of Waves of Finite Longitudinal Disturbances. En: Philosophical Transactions of the Royal Society (1870), p. 277–288Riemann, B.: Über die Fortpflanzung ebener Luftwellen von endlicher Schwingungsweite. En: Göttinger Nachrichten (1860), p. 192–197Risebro, N. H.: A front-tracking alternative to the random choice method. En: Proceedings of the American Mathematical Society 117 (1993), Nr. 4, p. 1125–1139Rudin, W.: Functional Analysis. MacGraw-Hill Science, 1991Schatzman, M.: Continuous Glimm functionals and uniqueness of solutions of the Riemann problem. En: Indiana University Mathematics Journal 34 (1985), Nr. 3, p. 533–589Sherwood, T. K. ; Pigford, R. L. ; Wilke, C. R.: Mass Transfer. Mac Graw-Hill, Chemical Engineering Series, 1975Smoller, J.: Shock waves and reaction-diffusion equations. Vol. 258. Springer Science & Business Media, 2012Webster, R.: Convexity. Oxford University Press, 1994Whittaker, E. T. ; Watson, G. N.: A Course of Modern Analysis: an Introduction to the General Theory of Infinite Processes and of Analytic Functions; with an Account of the Principal Transcendental Functions. Cambridge University Press, 1928Yartsev, A.: Diffusion of gases through the alveolar membrane. 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