Date:
Speaker : Changpin Li, Shanghai University, Shanghai 200444, China
Time : 13:00 - 14:00 CET (Rome/Paris)
Hosted at: SISSA, International School of Advanced Studies, Trieste, Italy
Zoom : A link will appear here
Organizers : Pavan Pranjivan Mehta* (pavan.mehta@sissa.it) and Arran Fernandez** (arran.fernandez@emu.edu.tr)
* SISSA, International School of Advanced Studies, Italy
** Eastern Mediterranean University, Northern Cyprus
Keywords: Super slow diffusion, Hadamard derivative, asymptotics, numerical computation
Abstract: The super slow diffusion indicates that the solution to the diffusion equation has algebraic asymptotics in the sense of logarithmic function. It is modelled by Hadamard derivatives. In this talk, we mainly introduce the logarithmic asymptotics and regularity of the solution to the Caputo-Hadamard fractional evolution equation. Based on these theoretical analysis, we construct the reliable numerical algorithms to numerically solve it, where various kinds of numerical algorithms for Caputo-Hadamard derivatives are also displayed.
Biography: Changpin Li earned his doctoral degree in computational mathematics from Shanghai University in 1998. He worked in the same univeristy and became full professor in 2007. He has been Chien Wei-zang Scholar (II) since 2020 and FIMA (Fellow of the Institute of Mathematics and its Applications, UK) since 2021. His main research interests include numerical methods for fractional partial differential equations and dynamics of fractional differential equations. He has presided over 8 NSFCs (National Natural Science Foundations of China). And he has published three monographs and more than 150 papers in SIAM jounrals, IMA J Appl Math, J Comput Phys, J Nonlinear Sci, J Sci Comput, PRE, Phys D, etc.
Bibliography
[1] C.P. Li, Z.Q. Li, Z. Wang. “Mathematical analysis and the local discontinuous Galerkin method %for Caputo-Hadamard fractional partial differential equation”. Journal of Scientific Computing 85(2) (2020), article 41.
[2] C.P. Li, Z.Q. Li., “Asymptotic behaviors of solution to Caputo-Hadamard fractional partial differential equation with fractional Laplacian”. International Journal of Computer Mathematics 98(2) (2021), pp. 305-339.
[3] C.P. Li, Z.Q. Li. “The blow-up and global existence of solution to Caputo-Hadamard fractional partial differential equation with fractional Laplacian”. Journal of Nonlinear Science 31(5) (2021), article 80.
[4] E.Y. Fan, C.P. Li, Z.Q. Li. “Numerical approaches to Caputo-Hadamard fractional derivatives with applications to long-term integration of fractional differential systems”. Communications in Nonlinear Science and Numerical Simulation 106 (2022), article 106096.
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