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Journal of the Optical Society of Korea
Journal Prestige (SJR): 0.297  Citation Impact (citeScore): 1 Number of Followers: 2  Open Access journalISSN (Print) 1226-4776 - ISSN (Online) 2093-6885 Published by Optical Society of America  [15 journals]
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- Uniform regularity for the isentropic compressible magneto-micropolar
system
Authors: Jishan Fan, Peng Wang, Yong Zhou
Pages: 519 - 527
Abstract: In this paper, we are concerned with the uniform regularity estimates of smooth solutions to the isentropic compressible magneto-micropolar system in
. Under the assumption that 
, and by applying the classic bilinear commutator and product estimates, the uniform estimates of solutions to the isentropic compressible magneto-micropolar system are established in 
space, 
.
PubDate: 2021-10-28
DOI: 10.3846/mma.2021.13632
Issue No: Vol. 26, No. 4 (2021)
- A subgrid stabilized method for Navier-Stokes equations with nonlinear
slip boundary conditions
Authors: Xiaoxia Dai, Chengwei Zhang
Pages: 528 - 547
Abstract: In this paper, we consider a subgrid stabilized Oseen iterative method for the Navier-Stokes equations with nonlinear slip boundary conditions and high Reynolds number. We provide one-level and two-level schemes based on this stability algorithm. The two-level schemes involve solving a subgrid stabilized nonlinear coarse mesh inequality system by applying m Oseen iterations, and a standard one-step Newton linearization problems without stabilization on the fine mesh. We analyze the stability of the proposed algorithm and provide error estimates and parameter scalings. Numerical examples are given to confirm our theoretical findings.
PubDate: 2021-10-28
DOI: 10.3846/mma.2021.12299
Issue No: Vol. 26, No. 4 (2021)
- Third-order generalized discontinuous impulsive problems on the half-line
Authors: Feliz Minhós, Rui Carapinha
Pages: 548 - 565
Abstract: In this paper, we improve the existing results in the literature by presenting weaker sufficient conditions for the solvability of a third-order impulsive problem on the half-line, having generalized impulse effects. More precisely, our nonlinearities do not need to be positive nor sublinear and the monotone assumptions are local ones. Our method makes use of some truncation and perturbed techniques and on the equiconvergence at infinity and the impulsive points. The last section contains an application to a boundary layer flow problem over a stretching sheet with and without heat transfer.
PubDate: 2021-10-28
DOI: 10.3846/mma.2021.12557
Issue No: Vol. 26, No. 4 (2021)
- Exponential Stability of laminated beam with constant delay feedback
Authors: Kassimu Mpungu, Tijani A. Apalara
Pages: 566 - 581
Abstract: In this article, we consider a system of laminated beams with an internal constant delay term in the transverse displacement. We prove that the dissipation through structural damping at the interface is strong enough to exponentially stabilize the system under suitable assumptions on delay feedback and coefficients of wave propagation speed.
PubDate: 2021-10-28
DOI: 10.3846/mma.2021.13759
Issue No: Vol. 26, No. 4 (2021)
- Analytic solutions of a two-fluid hydrodynamic model
Authors: Imre Ferenc Barna, László Mátyás
Pages: 582 - 590
Abstract: We investigate a one dimensional flow described with the non-compressible coupled Euler and non-compressible Navier-Stokes equations in the Cartesian coordinate system. We couple the two fluids through the continuity equation where different void fractions can be considered. The well-known self-similar Ansatz was applied and analytic solutions were derived for both velocity and pressure field as well.
PubDate: 2021-10-28
DOI: 10.3846/mma.2021.13637
Issue No: Vol. 26, No. 4 (2021)
- Self-similarity techniques for chaotic attractors with many scrolls using
step series switching
Authors: Emile Franc Doungmo Goufo, Chokkalingam Ravichandran, Gunvant A. Birajdar
Pages: 591 - 611
Abstract: Highly applied in machining, image compressing, network traffic prediction, biological dynamics, nerve dendrite pattern and so on, self-similarity dynamic represents a part of fractal processes where an object is reproduced exactly or approximately exact to a part of itself. These reproduction processes are also very important and captivating in chaos theory. They occur naturally in our environment in the form of growth spirals, romanesco broccoli, trees and so on. Seeking alternative ways to reproduce self-similarity dynamics has called the attention of many authors working in chaos theory since the range of applications is quite wide. In this paper, three combined notions, namely the step series switching process, the Julia’s technique and the fractal-fractional dynamic are used to create various forms of self-similarity dynamics in chaotic systems of attractors, initially with two, five and seven scrolls. In each case, the solvability of the model is addressed via numerical techniques and related graphical simulations are provided. It appears that the initial systems are able to trigger a self-similarity process that generates the exact or approximately exact copy of itself or part of itself. Moreover, the dynamics of the copies are impacted by some model’s parameters involved in the process. Using mathematical concepts to re-create features that usually occur in a natural way proves to be a prowess as related applications are many for engineers.
PubDate: 2021-11-26
DOI: 10.3846/mma.2021.13678
Issue No: Vol. 26, No. 4 (2021)
- On the maximum number of period annuli for second order conservative
equations
Authors: Armands Gritsans, Inara Yermachenko
Pages: 612 - 630
Abstract: We consider a second order scalar conservative differential equation whose potential function is a Morse function with a finite number of critical points and is unbounded at infinity. We give an upper bound for the number of nonglobal nontrivial period annuli of the equation and prove that the upper bound obtained is sharp. We use tree theory in our considerations.
PubDate: 2021-11-26
DOI: 10.3846/mma.2021.13979
Issue No: Vol. 26, No. 4 (2021)
- Differential equations with tempered Ψ-Caputo fractional derivative
Authors: Milan Medveď, Eva Brestovanská
Pages: 631 - 650
Abstract: In this paper we define a new type of the fractional derivative, which we call tempered Ψ−Caputo fractional derivative. It is a generalization of the tempered Caputo fractional derivative and of the Ψ−Caputo fractional derivative. The Cauchy problem for fractional differential equations with this type of derivative is discussed and some existence and uniqueness results are proved. We present a Henry-Gronwall type inequality for an integral inequality with the tempered Ψ−fractional integral. This inequality is applied in the proof of an existence theorem. A result on a representation of solutions of linear systems of Ψ−Caputo fractional differential equations is proved and in the last section an example is presented.
PubDate: 2021-11-26
DOI: 10.3846/mma.2021.13252
Issue No: Vol. 26, No. 4 (2021)
- On singular solutions of the stationary Navier-Stokes system in power cusp
domains
Authors: Konstantinas Pileckas, Alicija Raciene
Pages: 651 - 668
Abstract: The boundary value problem for the steady Navier–Stokes system is considered in a 2D bounded domain with the boundary having a power cusp singularity at the point O. The case of a boundary value with a nonzero flow rate is studied. In this case there is a source/sink in O and the solution necessarily has an infinite Dirichlet integral. The formal asymptotic expansion of the solution near the singular point is constructed and the existence of a solution having this asymptotic decomposition is proved.
PubDate: 2021-11-26
DOI: 10.3846/mma.2021.13836
Issue No: Vol. 26, No. 4 (2021)
- An existence result for quasilinear parabolic systems with lower order
terms
Authors: Farah Balaadich, Elhoussine Azroul
Pages: 669 - 683
Abstract: In this paper we prove the existence of weak solutions for a class of quasilinear parabolic systems, which correspond to diffusion problems, in the form
where Ω is a bounded open domain of 
be given and 
The function v belongs to
is in a moving and dissolving substance, the dissolution is described by f and the motion by g. We prove the existence result by using Galerkin’s approximation and the theory of Young measures.
PubDate: 2021-11-26
DOI: 10.3846/mma.2021.13553
Issue No: Vol. 26, No. 4 (2021)
- Numerical validation of probabilistic laws to evaluate finite element
error estimates
Authors: Jöel Chaskalovic, Franck Assous
Pages: 684 - 695
Abstract: We propose a numerical validation of a probabilistic approach applied to estimate the relative accuracy between two Lagrange finite elements Pk and Pm,(k < m). In particular, we show practical cases where finite element Pk gives more accurate results than finite element Pm. This illustrates the theoretical probabilistic framework we recently derived in order to evaluate the actual accuracy. This also highlights the importance of the extra caution required when comparing two numerical methods, since the classical results of error estimates concerns only the asymptotic convergence rate.
PubDate: 2021-11-26
DOI: 10.3846/mma.2021.14079
Issue No: Vol. 26, No. 4 (2021)
