Browsing by Author "Taskesen, Hatice"

Now showing 1 - 8 of 8

Conservation Laws for a Model With Both Cubic and Quadratic Nonlinearity
(2019) Alaloush, Mohanad; Taskesen, Hatice
In this paper, the conservation laws for a model with both quadratic and cubic nonlinearity$m_t\\;=\\;bu_x\\;+\\;\\frac12a\\;{\\left[(u^2-u_x^2\\;m)\\right]}_x+\\frac12c\\;(2m.\\;u_x+m_x.u);\\;m=u-u_{xx}$are considered for the six cases of coefficients. By using a variational derivative approach,conservation laws were constructed. The computations to derive multipliers and conservation law fluxes are conducted by using a Maple-based package which is called GeM.
Elastoplastik-mikro Yapı Modellerinde Ortaya Çıkan Doğrusal Olmayan Evolüsyon Denklemi İçin Varlık Sonuçları
(2019) Taskesen, Hatice
Bu çalışmada, sınırlı bir alanda elastoplastik-mikroyapı modellerinde ortaya çıkan doğrusal olmayan bir evrim denklemi için global varlık sonuçları potential well metodu kullanılarak oluşturulmuştur. Potential well yöntemi için bir fonksiyonel tanımlanmış ve bu fonksiyonelin işaret değişmezliği kullanılarak yüksek başlangıç enerjili durumda global varlık kanıtlanmıştır.
Existence Results for a Nonlinear Timoshenko Equation With High Initial Energy
(Amer inst Physics, 2015) Taskesen, Hatice; Polat, Necat
The aim of the present paper is to study the initial -boundary value problem for a nonlinear Timoshenko equation with high energy initial data. Existence of global weak solutions is proved by sign preserving property of a new functional which is introduced for the potential well method.
Global Existence and Decay of Solutions for the Generalized Bad Boussinesq Equation
(Zhejiang Univ, Editorial Committee Applied Mathematics, 2013) Taskesen, Hatice; Polat, Necat; Ertas, Abdulkadir
In this paper, we consider the global existence of solutions for the Cauchy problem of the generalized sixth order bad Boussinesq equation. Moreover, we show that the supremum norm of the solution decays algebraically to zero as (1 + t)(-(1/7)) when t approaches to infinity, provided the initial data are sufficiently small and regular.
On the Existence of Global Solutions for a Nonlinear Klein-Gordon Equation
(Univ Nis, Fac Sci Math, 2014) Polat, Necat; Taskesen, Hatice
The aim of this work is to study the global existence of solutions for the Cauchy problem of a Klein-Gordon equation with high energy initial data. The proof relies on constructing a new functional, which includes both the initial displacement and the initial velocity: with sign preserving property of the new functional we show the existence of global weak solutions.
On the Impact of Noise on Hyperbolic-Type Traveling Wave Solutions of Some Stochastic Evolution Equations
(World Scientific Publ Co Pte Ltd, 2022) Taskesen, Hatice; Alaloush, Mohanad
In this paper, traveling wave solutions of some nonlinear stochastic evolution equations emerging in miscellaneous fields such as modeling of flame propagation, magneto-acoustic waves in plasma and small-amplitude water waves with surface tension are investigated. By means of Galilean transformation and tanh method, we obtain some exact solutions such as kink wave solution, solitary wave solution and periodic solution. To illustrate the impact of noise on the solutions, we assigned different noise functions for the external noise. The results showed that the waveform deforms as the noise intensity increases.
On the Peakon Solutions of Some Stochastic Nonlinear Evolution Equations
(Springer, 2021) Yokus, Asif; Taskesen, Hatice; Alaloush, Mohanad; Demirdag, Betul Deniz
In this paper, stochastic Fornberg-Whitham and a stochastic Camassa-Holm (CH) type equations are studied. A Galilean transformation which previously used for a stochastic KdV equation is employed to transform the equations into their deterministic counterparts. Then (1/G')-expansion method is used to obtain analytical solutions. 2D, 3D, and contour graphs representing the peakon solutions have been plotted by assigning special values to the constants in the solutions via computer software. In addition, by giving different random values to the external noise, the effect of the noise on the wave-forms has been exhibited. The obtained results have been discussed in detail.
Qualitative Results for a Relativistic Wave Equation With Multiplicative Noise and Damping Terms
(Amer inst Mathematical Sciences-aims, 2023) Taskesen, Hatice
Wave equations describing a wide variety of wave phenomena are commonly seen in mathematical physics. The inclusion of a noise term in a deterministic wave equation allows neglected degrees of freedom or fluctuations of external fields describing the environment to be considered in the equation. Moreover, adding a noise term to the deterministic equation reveals remarkable new features in the qualitative behavior of the solution. For example, noise can lead to singularities in some equations and prevent singularities in others. Taking into account the effects of the fluctuations along with a space-time white noise, we consider a relativistic wave equation with weak and strong damping terms and investigate the effect of multiplicative noise on the behavior of solutions. The existence of local and global solutions is provided, and some qualitative properties of solutions, such as continuous dependence of solutions on initial data, and blow up of solutions, are given. Moreover, an upper bound is provided for the blow up time.