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On the Boundedness of Solution of the Parabolic Differential Equation with Time Involution

Allaberen Ashyralyev1, 2, 3 and Amer Ahmed*1


1 Department of Mathematics, Near East University, Nicosia, Mersin 10, Turkey.

2 Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St,Moscow 117198, Russian Federation.

3 Institute of Mathematics and Mathematical Modeling, 050010, Almaty,Kazakhstan.

*Corresponding author’s e-mail: [email protected] and [email protected]*

Original: 7 August 2020        Revised: 14 septembre 2020        Accepted: 26 September 2020        Published online: 20 December 2020  

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In the present paper, the initial value problem for the parabolic type involutory partial differential equation is investigated. Applying Green’s function of space operator generated by the differential problem, we get formula for solution of this problem. The theorem on the existence and uniqueness of bounded solution of the nonlinear problem with involution is established.

Key Words: Hilbert space, Boundedness, Involution, Parabolic equation