Variational Formulation and A Priori Estimates for the Galerkin Method for a Fractional Diffusion Equation

M. E. de S. Lima, E. C. de Oliveira, A. da C. Viana

Abstract


In this work we obtain a variational formulation and {\it a priori} estimates for approximate solutions of a problem involving fractional diffusion equations.

Keywords


Galerkin method, fractional diffusion equation, {\it a priori} estimates.

Full Text:

PDF

References


P. Biler, T. Funaki & W.A. Woyczynski. Fractal Burgers equations. Journal of Differential Equations, 148(1) (1998), 9–46.

M.P. Bonkile, A. Awasthi, C. Lakshmi, V. Mukundan & V. Aswin. A systematic literature review of Burgers’ equation with recent advances. Pramana, 90(6) (2018), 1–21.

L. Djilali & A. Rougirel. Galerkin method for time fractional diffusion equations. Journal of Elliptic and Parabolic Equations, 4(2) (2018), 349–368.

L.C. Evans. Partial Differential Equations. Graduate Studies in Mathematics, 19(4) (1998), 7.

J. Kemppainen, J. Siljander, V. Vergara & R. Zacher. Decay estimates for time-fractional and other non-local in time subdiffusion equations in Rd. Mathematische Annalen, 366(3) (2016), 941–979.

A.A. Kilbas, H.M. Srivastava & J.J. Trujillo. “Theory and Applications of Fractional Differential Equations”, volume 204. Elsevier (2006).

A. Lischke, G. Pang, M. Gulian, F. Song, C. Glusa, X. Zheng, Z. Mao, W. Cai, M.M. Meerschaert, M. Ainsworth et al. What is the fractional Laplacian? A comparative review with new results. Journal of Computational Physics, 404 (2020), 109009.

R. Metzler & J. Klafter. The random walk’s guide to anomalous diffusion: a fractional dynamics approach. Physics Reports, 339(1) (2000), 1–77.

W.R. Schneider &W.Wyss. Fractional diffusion and wave equations. Journal of Mathematical Physics, 30(1) (1989), 134–144.




DOI: https://doi.org/10.5540/tcam.2022.023.04.00673

Article Metrics

Metrics Loading ...

Metrics powered by PLOS ALM

Refbacks

  • There are currently no refbacks.


Trends in Computational and Applied Mathematics

A publication of the Brazilian Society of Applied and Computational Mathematics (SBMAC)

 

Indexed in:

                       

         

 

Desenvolvido por:

Logomarca da Lepidus Tecnologia