Exponential decay of solutions with \(L^{p}\) -norm for a class to semilinear wave equation with damping and source terms
OMA-Vol. 4 (2020), Issue 2, pp. 123 – 131 Open Access Full-Text PDF
Amar Ouaoua, Messaoud Maouni, Aya Khaldi
Abstract: In this paper, we consider an initial value problem related to a class of hyperbolic equation in a bounded domain is studied. We prove local existence and uniqueness of the solution by using the Faedo-Galerkin method and that the local solution is global in time. We also prove that the solutions with some conditions exponentially decay. The key tool in the proof is an idea of Haraux and Zuazua with is based on the construction of a suitable Lyapunov function.
On sufficient conditions for a graph to be \(k\)-path-coverable, \(k\)-edge-hamiltonian, Hamilton-connected, traceable and \(k^{-}\)-independent
ODAM-Vol. 3 (2020), Issue 3, pp. 66 – 76 Open Access Full-Text PDF
Junjiang Li, Guifu Su, Huichao Shi, Fuguo Liu
Abstract: The inverse degree of a graph was defined as the sum of the inverses of the degrees of the vertices. In this paper, we focus on finding sufficient conditions in terms of the inverse degree for a graph to be \(k\)-path-coverable, \(k\)-edge-hamiltonian, Hamilton-connected and traceable, respectively. The results obtained are not dropped.
Quantum mechanical methods for advancement of hydrophysical engineering
EASL-Vol. 3 (2020), Issue 4, pp. 55 – 59 Open Access Full-Text PDF
Jonah Lissner
Abstract: Quantum mechanical mathematical methods are utilized for theoretical engineering and testing of hydrocellular engineering for quantum computation criteria and quantum power engineering.
Homomorphism of intuitionistic fuzzy multigroups
OMS-Vol. 4 (2020), Issue 1, pp. 430 – 441 Open Access Full-Text PDF
I. M. Adamu
Abstract: This paper introduces the concept of homomorphism in intuitionistic fuzzy multigroups context. It also investigates Some homomorphic properties of intuitionistic fuzzy multigroups. It is shown that the homomorphic image and homomorphic preimage of intuitionistic fuzzy multigroups are also intuitionistic fuzzy multigroups. Finally, it presents some homomorphic properties of normalizer of intuitionistic fuzzy multigroups.
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.
