On Solutions of A Parabolic Partial Differential Equation of Neutral Type Including Piecewise Continuous Time Delay

Authors : Zekeriya Özkan, Duygu Aruğaslan Çinçin, Marat Akhmet

Pages : 29-35

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Publication Date : 2023-07-31

Article Type : Research Article

Abstract :There have been very few studies on partial differential equations including piecewise constant arguments and generalized piecewise constant arguments. However, as far as we know, there is no study conducted on neutral type partial differential equations including piecewise constant argument of generalized type. With this motivation, we discuss the solution and analysis of a parabolic partial differential equation of neutral type including generalized piecewise constant delay. The aim of this study is to investigate detailed and well-defined qualitative properties of this equation. The formal solution of the handled equation is obtained by using the separation of variables method. Since there exist the piecewise constant arguments, we get an ordinary differential equation with respect to the time variable on each consecutive intervals and then apply the Laplace transform method using the unit step function and method of steps. With the help of the qualitative properties of the solutions of the obtained differential equation, unboundedness and oscillations of the solutions of the issue problem can be investigated.
Keywords : kısmi diferansiyel denklem, nötr tip, parçalı sabit argüman, laplace dönüşümü, salınım, sınırsızlık