Stability of stochastic 2D Navier-Stokes equations with memory and Poisson jumps
OMS-Vol. 4 (2020), Issue 1, pp. 417 – 429 Open Access Full-Text PDF
Diem Dang Huan
Abstract: The objective of this paper is to study the stability of the weak solutions of stochastic 2D Navier-Stokes equations with memory and Poisson jumps. The asymptotic stability of the stochastic Navier-Stoke equation as a semilinear stochastic evolution equation in Hilbert spaces is obtained in both mean square and almost sure senses. Our results can extend and improve some existing ones.
Stochastic dynamic for an extensible beam equation with localized nonlinear damping and linear memory
OMS-Vol. 4 (2020), Issue 1, pp. 400 – 416 Open Access Full-Text PDF
Abdelmajid Ali Dafallah, Fadlallah Mustafa Mosa, Mohamed Y. A. Bakhet, Eshag Mohamed Ahmed
Abstract: In this paper, we concerned to prove the existence of a random attractor for the stochastic dynamical system generated by the extensible beam equation with localized non-linear damping and linear memory defined on bounded domain. First we investigate the existence and uniqueness of solutions, bounded absorbing set, then the asymptotic compactness. Longtime behavior of solutions is analyzed. In particular, in the non-autonomous case, the existence of a random attractor attractors for solutions is achieved.
On the non-linear diophantine equation \({\boldsymbol{379}}^{\boldsymbol{x}}\boldsymbol{+}{\boldsymbol{397}}^{\boldsymbol{y}}\boldsymbol{=}{\boldsymbol{z}}^{\boldsymbol{2}}\)
OMS-Vol. 4 (2020), Issue 1, pp. 397 – 399 Open Access Full-Text PDF
Sudhanshu Aggarwal, Nidhi Sharma
Abstract: In this article, authors discussed the existence of solution of non-linear diophantine equation \({379}^x+{397}^y=z^2,\) where \(x,y,z\) are non-negative integers. Results show that the considered non-linear diophantine equation has no non-negative integer solution.
Bayesian latent autoregressive stochastic volatility: an application of naira to eleven exchangeable currencies rates
OMS-Vol. 4 (2020), Issue 1, pp. 386 – 396 Open Access Full-Text PDF
R. O. Olanrewaju, J. F. Ojo, L. O. Adekola
Abstract: This paper provides a procedure for estimating Stochastic Volatility (SV) in financial time series via latent autoregressive in a Bayesian setting. A Gaussian distributional combined prior and posterior of all hyper-parameters (autoregressive coefficients) were specified such that the Markov Chain Monte Carlo (MCMC) iterative procedure via the Gibbs and Metropolis-Hasting sampling method was used in estimating the resulting exponentiated forms (quadratic forms) from the posterior kernel density. A case study of Naira to eleven (11) exchangeable currencies$^,$ rates by Central Bank of Nigeria (CBN) was subjected to the estimated solutions of the autoregressive stochastic volatility. The posterior volatility estimates at 5%, 50%, and 95% quantiles of \({e^{\frac{\mu }{2}}}\) = (0.130041, 0.1502 and 0.1795) respectively unveiled that the Naira-US Dollar exchange rates has the highest rates bartered by fluctuations.
Global solutions and general decay for the dispersive wave equation with memory and source terms
OMA-Vol. 4 (2020), Issue 2, pp. 116 – 122 Open Access Full-Text PDF
Mohamed Mellah
Abstract: This paper concerns with the global solutions and general decay to an initial-boundary value problem of the dispersive wave equation with memory and source terms.
Controllability for some nonlinear impulsive partial functional integrodifferential systems with infinite delay in Banach spaces
OMA-Vol. 4 (2020), Issue 2, pp. 104 – 115 Open Access Full-Text PDF
Patrice Ndambomve, Khalil Ezzinbi
Abstract: This work concerns the study of the controllability for some impulsive partial functional integrodifferential equation with infinite delay in Banach spaces. We give sufficient conditions that ensure the controllability of the system by supposing that its undelayed part admits a resolvent operator in the sense of Grimmer, and by making use of the measure of noncompactness and the Mönch fixed-point Theorem. As a result, we obtain a generalization of the work of K. Balachandran and R. Sakthivel (Journal of Mathematical Analysis and Applications, 255, 447-457, (2001)) and a host of important results in the literature, without assuming the compactness of the resolvent operator. An example is given for illustration.
