Dear colleagues and researchers,
The Journal of the Korean Society for Industrial and Applied Mathematics (J-KSIAM) Volume 26 Number 2 (June 2022 issue) has been posed on KSIAM Journal Archive or other information on the journal is available on the KSIAM website http://www.ksiam.org or https://ksiam.org/journal/journal01.asp.
The journal is one of Korea Citation Indexed (KCI) journals since 2007 and is indexed in Emerging Sources Citation Index (ESCI) since 2017.
Readers interested in the following articles may download each of articles free of charge from our website and authors are encouraged to submit a paper via the online submission site.
Jae Hoon Jung, Editor-in-Chief
Min Seok Choi, Gun Jin Yun, Managing Editors
EXISTENCE AND DECAY PROPERTIES OF WEAK SOLUTIONS TO THE INHOMOGENEOUS HALL-MAGNETOHYDRODYNAMIC EQUATIONS
PIGONG HAN, KEKE LEI, HENGGANG LIU, AND XUEWEN WANG
In this paper, we study the temporal decay of global weak solutions to the inhomogeneous Hall-magnetohydrodynamic (Hall-MHD) equations. First, an approximation problem and its weak solutions are obtained via the Caffarelli-Kohn-Nirenberg retarded molliﬁcation technique. Then, we prove that the approximate solutions satisfy uniform decay estimates. Finally, using the weak convergence method, we construct weak solutions with optimal decay rates to the inhomogeneous Hall-MHD equations.
FINITE SPEED OF PROPAGATION IN DEGENERATE EINSTEIN BROWNIAN MOTION
ISANKA GARLI HEVAGE AND AKIF IBRAGIMOV
We considered qualitative behaviour of the generalization of Einstein’s model of Brownian motion when the key parameter of the time interval of free jump degenerates. Fluids will be characterised by number of particles per unit volume (density of ﬂuid) at point of observation. Degeneration of the phenomenon manifests in two scenarios: a) ﬂow of the ﬂuid, which is highly dispersing like a non-dense gas and b) ﬂow of ﬂuid far away from the source of ﬂow, when the velocity of the ﬂow is incomparably smaller than the gradient of the density. First, we will show that both types of ﬂows can be modeled using the Einstein paradigm. We will investigate the question: What features will particle ﬂow exhibit if the time interval of the free jump is inverse proportional to the density and its gradient? We will show that in this scenario, the ﬂow exhibits localization property, namely: if at some moment of time t0 in the region, the gradient of the density or density itself is equal to zero, then for some T during time interval [t0, t0 + T] there is no ﬂow in the region. This directly links to Barenblatt’s ﬁnite speed of propagation property for the degenerate equation. The method of the proof is very different from Barenblatt’s method and based on the application of Ladyzhenskaya - De Giorgi iterative scheme and Vespri - Tedeev technique. From PDE point of view it assumed that solution exists in appropriate Sobolev type of space.
AN EFFICIENT METHOD FOR SOLVING TWO-ASSET TIME FRACTIONAL BLACK-SCHOLES OPTION PRICING MODEL
R. DELPASAND AND M. M. HOSSEINI
In this paper, we investigate an efﬁcient hybrid method for solving two-asset time fractional Black-Scholes partial differential equations. The proposed method is based on the Crank-Nicolson the radial basis functions methods. We show that, this method is convergent and we obtain good approximations for solution of our problems. The numerical results show high accuracy of the proposed method without needing high computational cost.