Tamkang Journal of Mathematics

Existence and decay estimate of global solution for a viscoelastic wave equation with nonlinear boundary source term

2024-01-26T07:49:32+00:00

In this paper, we consider a viscoelastic wave equation with nonlinear boundary source term. By the combination of Galerkin approximation and potential well methods, we prove the global existence of solutions. Then, we give an decay rate estimate of the energy by making use of the perturbed energy method.

Addendum to: Solving an inverse problem for the Sturm-Liouville operator with singular potential by Yurko's method (Tamkang J. Math. 52 (2021), no. 1, 125-154)

2024-05-10T07:07:37+00:00

This addendum outlines a simpler proof of Theorem 2.1 from [N.P. Bondarenko, Tamkang J. Math. 52(1), 125-154 (2021)].

On the well-posedness and stability analysis of standing waves for a 1D-Benney-Roskes system

2024-01-17T12:04:36+00:00

In this paper, we revisit the well-posedness for the Benney-Roskes system (also known as Zakharov-Rubenchik systems) for N = 1, 2, 3, and establish the nonlinear orbital stability of ground state standing waves in the case N = 1, by using the variational approach induced by the Hamiltonian structure and the Liapunov method.

Adaptive mesh extended cubic B-spline method for singularly perturbed delay Sobolev problems

2024-03-13T06:29:29+00:00

The purpose of this paper is to develop a robust numerical scheme for a class of singularly perturbed delay Sobolev (pseudo-parabolic) problems that have wide application in various branches of mathematical physics and fluid mechanics.
For the small perturbation parameter, the standard numerical schemes for the solution of these problems fail to resolve the boundary layer(s) and the oscillations occur near the boundary layer. Thus, in this paper to resolve the boundary layer(s), im-
plicit Euler scheme for the time derivatives on uniform mesh and extended B-spline basis functions consisting of free parameter λ are presented for spatial variable on Bakhvalov type mesh. The stability and uniform convergence analyisis of the pro
posed method are established. The error estimation of the developed method is shown to be firts order accurate in time and second order accurate in space. Numerical exprementation is carried out to validate the applicability of the developed
numerical method. The numerical results reveals that the computational result is in agreement with the theoretical estimations

Certain coefficient problems of $\mathcal{S}_{e}^{*}$ and $\mathcal{C}_{e}$

2023-10-02T05:22:36+00:00

In this current study, we consider the classes $\mathcal{S}^{*}_{e}$ and $\mathcal{C}_e$ to obtain sharp bounds for the third Hankel determinant for functions within these classes. Additionally, we provide estimates for the sixth and seventh coefficients while establishing the fourth-order Hankel determinant as well.

Existence theory for a fractional q-integral equations

2024-04-25T03:24:41+00:00

The paper focuses on establishing sufficient conditions for the existence of the solutions for a functional equation involving q-fractional integrals, particularly in Banach spaces. In this method, the technique of measures of noncompactness and Petryshyn’s fixed point theorem Banach space is used. We provide some examples of equations, which confirm that our result is applicable to a wide class of integral equations.