IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i1p57-d304359.html
   My bibliography  Save this article

Mathematical Analysis of a Thermostatted Equation with a Discrete Real Activity Variable

Author

Listed:
  • Carlo Bianca

    (Laboratoire Quartz EA 7393, École Supérieure d’Ingénieurs en Génie Électrique, Productique et Management Industriel, 95092 Cergy Pontoise CEDEX, France
    Laboratoire de Recherche en Eco-innovation Industrielle et Energétique, École Supérieure d’Ingénieurs en Génie Électrique, Productique et Management Industriel, 95092 Cergy Pontoise CEDEX, France)

  • Marco Menale

    (Laboratoire Quartz EA 7393, École Supérieure d’Ingénieurs en Génie Électrique, Productique et Management Industriel, 95092 Cergy Pontoise CEDEX, France
    Dipartimento di Matematica e Fisica, Università degli Studi della Campania “L. Vanvitelli”, Viale Lincoln 5, I-81100 Caserta, Italy)

Abstract

This paper deals with the mathematical analysis of a thermostatted kinetic theory equation. Specifically, the assumption on the domain of the activity variable is relaxed allowing for the discrete activity to attain real values. The existence and uniqueness of the solution of the related Cauchy problem and of the related non-equilibrium stationary state are established, generalizing the existing results.

Suggested Citation

  • Carlo Bianca & Marco Menale, 2020. "Mathematical Analysis of a Thermostatted Equation with a Discrete Real Activity Variable," Mathematics, MDPI, vol. 8(1), pages 1-8, January.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:1:p:57-:d:304359
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/1/57/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/1/57/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Carlo Bianca & Caterina Mogno, 2018. "Modelling pedestrian dynamics into a metro station by thermostatted kinetic theory methods," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 24(2), pages 207-235, March.
    2. Giorno, Virginia & Spina, Serena, 2016. "Rumor spreading models with random denials," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 569-576.
    Full references (including those not matched with items on IDEAS)

    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.
    1. Tingqiang Chen & Lei Wang & Jining Wang & Qi Yang, 2017. "A Network Diffusion Model of Food Safety Scare Behavior considering Information Transparency," Complexity, Hindawi, vol. 2017, pages 1-16, December.
    2. Lu, Peng, 2019. "Heterogeneity, judgment, and social trust of agents in rumor spreading," Applied Mathematics and Computation, Elsevier, vol. 350(C), pages 447-461.
    3. Mikhail Kolev, 2019. "Mathematical Analysis of an Autoimmune Diseases Model: Kinetic Approach," Mathematics, MDPI, vol. 7(11), pages 1-14, October.
    4. Carlo Bianca & Marco Menale, 2022. "On the Existence of Self-Similar Solutions in the Thermostatted Kinetic Theory with Unbounded Activity Domain," Mathematics, MDPI, vol. 10(9), pages 1-14, April.
    5. Chen, Guanghua, 2019. "ILSCR rumor spreading model to discuss the control of rumor spreading in emergency," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 522(C), pages 88-97.
    6. Lu, Peng & Deng, Liping & Liao, Hongbing, 2019. "Conditional effects of individual judgment heterogeneity in information dissemination," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 335-344.
    7. Maria Gamboa & Maria Jesus Lopez-Herrero, 2018. "On the Number of Periodic Inspections During Outbreaks of Discrete-Time Stochastic SIS Epidemic Models," Mathematics, MDPI, vol. 6(8), pages 1-13, July.
    8. Antonio Di Crescenzo & Paola Paraggio & Serena Spina, 2023. "Stochastic Growth Models for the Spreading of Fake News," Mathematics, MDPI, vol. 11(16), pages 1-23, August.
    9. Sana Abdulkream Alharbi & Azmin Sham Rambely, 2020. "A New ODE-Based Model for Tumor Cells and Immune System Competition," Mathematics, MDPI, vol. 8(8), pages 1-14, August.
    10. Bruno Carbonaro & Marco Menale, 2019. "Dependence on the Initial Data for the Continuous Thermostatted Framework," Mathematics, MDPI, vol. 7(7), pages 1-11, July.
    11. Liu, Shang & Li, Peiyu, 2020. "Nonlinear analysis of pedestrian flow Reynolds number in video scenes," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    12. Lu, Peng & Yao, Qi & Lu, Pengfei, 2019. "Two-stage predictions of evolutionary dynamics during the rumor dissemination," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 517(C), pages 349-369.
    13. Jiang, Guoyin & Li, Saipeng & Li, Minglei, 2020. "Dynamic rumor spreading of public opinion reversal on Weibo based on a two-stage SPNR model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 558(C).
    14. Qi Yang & Yuejuan Hou & Haoran Wei & Tingqiang Chen & Jining Wang, 2022. "Nonlinear Diffusion Evolution Model of Unethical Behavior among Green Food Enterprise," Sustainability, MDPI, vol. 14(23), pages 1-22, December.

    Corrections

    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:gam:jmathe:v:8:y:2020:i:1:p:57-:d:304359. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.