Existence, Decay, and Blow-up of Solutions for a Weighted m -Biharmonic Equation with Nonlinear Damping and Source Terms

Ercan ÇELİK

In this paper, we consider the weighted m-biharmonic equation with nonlinear damping and source terms. We proved the global existence of solutions. Later, the decay of the energy is established by using Nakao's inequality. Finally, we proved the blow-up of solutions in finite time.

Статья 2024 Fen Fakültesi Journal of Function Spaces2024 12 Просмотры

An approximate solution of singularly perturbed problem on uniform mesh

Ercan ÇELİK

In this study, we obtain approximate solution for singularly perturbed problem of differential equation having two integral boundary conditions. With this purpose, we propose a new finite difference scheme. First, we construct this exponentially difference scheme on a uniform mesh using the finite difference method. We use the quasilinearization method and the interpolating quadrature formulas to establish the numerical scheme. Then, as a result of the error analysis, we show that the method under study is convergent in the first order. Consequently, theoretical findings are supported by numer ...Более

Статья 2024 Fen Fakültesi International Journal of Optimization and Control: Theories & Applications14 ( 1 ) 2 Просмотры

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Existence, Decay, and Blow-up of Solutions for a Weighted m -Biharmonic Equation with Nonlinear Damping and Source Terms

Ercan ÇELİK

An approximate solution of singularly perturbed problem on uniform mesh

Ercan ÇELİK