Journal Articles - Engineering - 2023

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Browsing Journal Articles - Engineering - 2023 by Author "ANH TUAN NGUYEN"
  • Publication
    GLOBAL WELL-POSEDNESS OF A CAUCHY PROBLEM FOR A NONLINEAR PARABOLIC EQUATION WITH MEMORY
    ( 2023)
    ANH TUAN NGUYEN
    ;
    BUI DAI NGHIA
    ;
    VAN THINH NGUYEN
    In this study, we examine a modified heat equation with memory and nonlinear source. The source function is considered under two different conditions, the global Lipschitz and the exponential growth functions. For the first condition, a special weighted Banach space is applied to deduce a desired result without any assumption on sufficiently small time and initial data. For the second condition of exponential growth, we apply the Moser–Trudinger inequality to cope with the source function, and a special time-space norm to deduce the unique existence of a global solution in regard to sufficiently small data. The main objective of this work is to prove the global existence and uniqueness of mild solutions. Besides the solution techniques, our main arguments are also based on the Banach fixed point theorem and linear estimates for the mild solution. The highlight of this study is that it is the first work on the global well-posedness for the mild solution of the fractional heat conduction with memory and nonlinear sources.
  • Publication
    TERMINAL VALUE PROBLEM FOR STOCHASTIC FRACTIONAL EQUATION WITHIN AN OPERATOR WITH EXPONENTIAL KERNEL
    ( 2023)
    NGUYEN DUC PHUONG
    ;
    LUU VU CAM HOAN
    ;
    DUMITRU BALEANU
    ;
    ANH TUAN NGUYEN
    In this paper, we investigate a terminal value problem for stochastic fractional diffusion equations with Caputo–Fabrizio derivative. The stochastic noise we consider here is the white noise taken value in the Hilbert space [Formula: see text]. The main contribution is to investigate the well-posedness and ill-posedness of such problem in two distinct cases of the smoothness of the Hilbert scale space [Formula: see text] (see Assumption 3.1), which is a subspace of [Formula: see text]. When [Formula: see text] is smooth enough, i.e. the parameter [Formula: see text] is sufficiently large, our problem is well-posed and it has a unique solution in the space of Hölder continuous functions. In contract, in the different case when [Formula: see text] is smaller, our problem is ill-posed; therefore, we construct a regularization result.