Nonlinear diffusion equation with reaction terms: Analytical and numerical results
Author
Abstract
Suggested Citation
DOI: 10.1016/j.amc.2018.02.040
Download full text from publisher
As the access to this document is restricted, you may want to search for a different version of it.
References listed on IDEAS
- Lenzi, E.K. & Menechini Neto, R. & Tateishi, A.A. & Lenzi, M.K. & Ribeiro, H.V., 2016. "Fractional diffusion equations coupled by reaction terms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 458(C), pages 9-16.
- P. H. Chavanis, 2008. "Nonlinear mean field Fokker-Planck equations. Application to the chemotaxis of biological populations," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 62(2), pages 179-208, March.
- Troncoso, P. & Fierro, O. & Curilef, S. & Plastino, A.R., 2007. "A family of evolution equations with nonlinear diffusion, Verhulst growth, and global regulation: Exact time-dependent solutions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 375(2), pages 457-466.
- T. Wada & A. M. Scarfone, 2009. "Asymptotic solutions of a nonlinear diffusive equation in the framework of κ-generalized statistical mechanics," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 70(1), pages 65-71, July.
- Zhou, Yanjun & Yin, Cangtao, 2016. "Power-law Fokker–Planck equation of unimolecular reaction based on the approximation to master equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 463(C), pages 445-451.
- Yin, Cangtao & Guo, Ran & Du, Jiulin, 2014. "The rate coefficients of unimolecular reactions in the systems with power-law distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 408(C), pages 85-95.
- Silva, A.T. & Lenzi, E.K. & Evangelista, L.R. & Lenzi, M.K. & da Silva, L.R., 2007. "Fractional nonlinear diffusion equation, solutions and anomalous diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 375(1), pages 65-71.
- Lenzi, E.K. & Mendes, R.S. & da Silva, L.R., 2000. "Statistical mechanics based on Renyi entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 280(3), pages 337-345.
- Plastino, A.R. & Casas, M. & Plastino, A., 2000. "A nonextensive maximum entropy approach to a family of nonlinear reaction–diffusion equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 280(3), pages 289-303.
- Plastino, A.R. & Plastino, A., 1995. "Non-extensive statistical mechanics and generalized Fokker-Planck equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 222(1), pages 347-354.
Most related items
These are the items that most often cite the same works as this one and are cited by the same works as this one.- Secrest, J.A. & Conroy, J.M. & Miller, H.G., 2020. "A unified view of transport equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 547(C).
- Pereira, A.P.P. & Fernandes, J.P. & Atman, A.P.F. & Acebal, J.L., 2018. "Parameter calibration between models and simulations: Connecting linear and non-linear descriptions of anomalous diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 369-382.
- Ou, Congjie & Huang, Zhifu & Chen, Jincan & El Kaabouchi, A. & Nivanen, L. & Le Méhauté, A. & Wang, Qiuping A., 2009. "A basic problem in the correlations between statistics and thermodynamics," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2313-2318.
- Ván, P, 2004. "One- and two-component fluids: restrictions from the Second Law," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 340(1), pages 418-426.
- Lucia, Umberto, 2010. "Maximum entropy generation and κ-exponential model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(21), pages 4558-4563.
- Alves, L.G.A. & Ribeiro, H.V. & Santos, M.A.F. & Mendes, R.S. & Lenzi, E.K., 2015. "Solutions for a q-generalized Schrödinger equation of entangled interacting particles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 429(C), pages 35-44.
- Iyiola, O.S. & Tasbozan, O. & Kurt, A. & Çenesiz, Y., 2017. "On the analytical solutions of the system of conformable time-fractional Robertson equations with 1-D diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 94(C), pages 1-7.
- Andrew Caplin & Mark Dean & John Leahy, 2022.
"Rationally Inattentive Behavior: Characterizing and Generalizing Shannon Entropy,"
Journal of Political Economy, University of Chicago Press, vol. 130(6), pages 1676-1715.
- Andrew Caplin & Mark Dean & John Leahy, 2017. "Rationally Inattentive Behavior: Characterizing and Generalizing Shannon Entropy," NBER Working Papers 23652, National Bureau of Economic Research, Inc.
- Ván, P., 2006. "Unique additive information measures—Boltzmann–Gibbs–Shannon, Fisher and beyond," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 365(1), pages 28-33.
- Zozor, S. & Vignat, C., 2007. "On classes of non-Gaussian asymptotic minimizers in entropic uncertainty principles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 375(2), pages 499-517.
- Ervin Kaminski Lenzi & Luiz Roberto Evangelista & Luciano Rodrigues da Silva, 2023. "Aspects of Quantum Statistical Mechanics: Fractional and Tsallis Approaches," Mathematics, MDPI, vol. 11(12), pages 1-15, June.
- Oikonomou, Th., 2007. "Tsallis, Rényi and nonextensive Gaussian entropy derived from the respective multinomial coefficients," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 386(1), pages 119-134.
- Bercher, J.-F., 2013. "Some properties of generalized Fisher information in the context of nonextensive thermostatistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(15), pages 3140-3154.
- Iulia-Elena Hirica & Cristina-Liliana Pripoae & Gabriel-Teodor Pripoae & Vasile Preda, 2022. "Lie Symmetries of the Nonlinear Fokker-Planck Equation Based on Weighted Kaniadakis Entropy," Mathematics, MDPI, vol. 10(15), pages 1-22, August.
- Moretto, Enrico & Pasquali, Sara & Trivellato, Barbara, 2016. "Option pricing under deformed Gaussian distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 446(C), pages 246-263.
- Oikonomou, Thomas & Tirnakli, Ugur, 2009. "Generalized entropic structures and non-generality of Jaynes’ Formalism," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 3027-3034.
- Sfetcu, Răzvan-Cornel, 2016. "Tsallis and Rényi divergences of generalized Jacobi polynomials," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 460(C), pages 131-138.
- Myrela Alves & David M. Garner & Anne M. G. G. Fontes & Luiz Vinicius de Alcantara Sousa & Vitor E. Valenti, 2018. "Linear and Complex Measures of Heart Rate Variability during Exposure to Traffic Noise in Healthy Women," Complexity, Hindawi, vol. 2018, pages 1-14, June.
- dos Santos, M.A.F. & Colombo, E.H. & Anteneodo, C., 2021. "Random diffusivity scenarios behind anomalous non-Gaussian diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
- Vignat, C. & Lamberti, P.W., 2012. "H-theorems for the Brownian motion on the hyperbolic plane," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(3), pages 544-551.
More about this item
Keywords
Anomalous diffusion; Nonlinear diffusion equation; Nonlinear fractional diffusion equation; Tsallis entropy;All these keywords.
Statistics
Access and download statisticsCorrections
All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:330:y:2018:i:c:p:254-265. See general information about how to correct material in RePEc.
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .
Please note that corrections may take a couple of weeks to filter through the various RePEc services.