IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i8p1283-d394083.html
   My bibliography  Save this article

Existence of a Unique Weak Solution to a Nonlinear Non-Autonomous Time-Fractional Wave Equation (of Distributed-Order)

Author

Listed:
  • Karel Van Bockstal

    (Research Group NaM 2 , Department of Electronics and Information systems, Ghent University, Krijgslaan 281, 9000 Ghent, Belgium)

Abstract

We study an initial-boundary value problem for a fractional wave equation of time distributed-order with a nonlinear source term. The coefficients of the second order differential operator are dependent on the spatial and time variables. We show the existence of a unique weak solution to the problem under low regularity assumptions on the data, which includes weakly singular solutions in the class of admissible problems. A similar result holds true for the fractional wave equation with Caputo fractional derivative.

Suggested Citation

  • Karel Van Bockstal, 2020. "Existence of a Unique Weak Solution to a Nonlinear Non-Autonomous Time-Fractional Wave Equation (of Distributed-Order)," Mathematics, MDPI, vol. 8(8), pages 1-16, August.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:8:p:1283-:d:394083
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/8/1283/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/8/1283/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Пигнастый, Олег & Koжевников, Георгий, 2019. "Распределенная Динамическая Pde-Модель Программного Управления Загрузкой Технологического Оборудования Производственной Линии [Distributed dynamic PDE-model of a program control by utilization of t," MPRA Paper 93278, University Library of Munich, Germany, revised 02 Feb 2019.
    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. Elisa Alòs & Maria Elvira Mancino & Tai-Ho Wang, 2019. "Volatility and volatility-linked derivatives: estimation, modeling, and pricing," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(2), pages 321-349, December.
    2. Jose Cruz & Daniel Sevcovic, 2020. "On solutions of a partial integro-differential equation in Bessel potential spaces with applications in option pricing models," Papers 2003.03851, arXiv.org.
    3. Ana Werlang & Gabriel Cunha & João Bastos & Juliana Serra & Bruno Barbosa & Luiz Barroso, 2021. "Reliability Metrics for Generation Planning and the Role of Regulation in the Energy Transition: Case Studies of Brazil and Mexico," Energies, MDPI, vol. 14(21), pages 1-27, November.
    4. Elena-Corina Cipu, 2019. "Duality Results in Quasiinvex Variational Control Problems with Curvilinear Integral Functionals," Mathematics, MDPI, vol. 7(9), pages 1-9, September.
    5. Hanno Gottschalk & Marco Reese, 2021. "An Analytical Study in Multi-physics and Multi-criteria Shape Optimization," Journal of Optimization Theory and Applications, Springer, vol. 189(2), pages 486-512, May.
    6. Assed Haddad & Ahmed Hammad & Danielle Castro & Diego Vasco & Carlos Alberto Pereira Soares, 2021. "Framework for Assessing Urban Energy Sustainability," Sustainability, MDPI, vol. 13(16), pages 1-18, August.
    7. Savin Treanţă, 2019. "On Locally and Globally Optimal Solutions in Scalar Variational Control Problems," Mathematics, MDPI, vol. 7(9), pages 1-8, September.
    8. Darvishi, M.T. & Najafi, Mohammad & Wazwaz, Abdul-Majid, 2021. "Conformable space-time fractional nonlinear (1+1)-dimensional Schrödinger-type models and their traveling wave solutions," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    9. Julien Hok & Sergei Kucherenko, 2021. "Pricing and Risk Analysis in Hyperbolic Local Volatility Model with Quasi Monte Carlo," Papers 2106.08421, arXiv.org.
    10. Ivan Francisco Yupanqui Tello & Alain Vande Wouwer & Daniel Coutinho, 2021. "A Concise Review of State Estimation Techniques for Partial Differential Equation Systems," Mathematics, MDPI, vol. 9(24), pages 1-15, December.
    11. Christian Klein & Julien Riton & Nikola Stoilov, 2021. "Multi-domain spectral approach for the Hilbert transform on the real line," Partial Differential Equations and Applications, Springer, vol. 2(3), pages 1-19, June.
    12. Marco Cirant & Roberto Gianni & Paola Mannucci, 2020. "Short-Time Existence for a General Backward–Forward Parabolic System Arising from Mean-Field Games," Dynamic Games and Applications, Springer, vol. 10(1), pages 100-119, March.
    13. Song, Xiaona & Wang, Mi & Song, Shuai & Wang, Zhen, 2021. "Observer-based sliding mode control for stochastic hyperbolic PDE systems with quantized output signal," Applied Mathematics and Computation, Elsevier, vol. 393(C).
    14. Mario Abundo & Enrica Pirozzi, 2019. "On the Integral of the Fractional Brownian Motion and Some Pseudo-Fractional Gaussian Processes," Mathematics, MDPI, vol. 7(10), pages 1-12, October.
    15. Christian Kuehn & Cinzia Soresina, 2020. "Numerical continuation for a fast-reaction system and its cross-diffusion limit," Partial Differential Equations and Applications, Springer, vol. 1(2), pages 1-26, April.
    16. Zaiping Zhu & Andres Iglesias & Liqi Zhou & Lihua You & Jianjun Zhang, 2022. "PDE-Based 3D Surface Reconstruction from Multi-View 2D Images," Mathematics, MDPI, vol. 10(4), pages 1-17, February.
    17. Andersson, Kristoffer & Oosterlee, Cornelis W., 2021. "A deep learning approach for computations of exposure profiles for high-dimensional Bermudan options," Applied Mathematics and Computation, Elsevier, vol. 408(C).
    18. Wei Zhou & Xingxing Hao & Kaidi Wang & Zhenyang Zhang & Yongxiang Yu & Haonan Su & Kang Li & Xin Cao & Arjan Kuijper, 2020. "Improved estimation of motion blur parameters for restoration from a single image," PLOS ONE, Public Library of Science, vol. 15(9), pages 1-21, September.
    19. Denny Ivanal Hakim & Yoshihiro Sawano, 2021. "Complex interpolation of variable Morrey spaces," Mathematische Nachrichten, Wiley Blackwell, vol. 294(11), pages 2140-2150, November.
    20. Knut K. Aase & Petter Bjerksund, 2021. "The Optimal Spending Rate versus the Expected Real Return of a Sovereign Wealth Fund," JRFM, MDPI, vol. 14(9), pages 1-36, September.

    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:8:p:1283-:d:394083. 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.