Scopus İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651

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Publisher: search.filters.publisher.SpringerSubject: search.filters.subject.Ill-Posed Problem

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Now showing 1 - 4 of 4
  • Article
    Citation - WoS: 10
    Citation - Scopus: 18
    Identifying the Space Source Term Problem for Time-Space Diffusion Equation
    (Springer, 2020) Karapinar, Erdal; Kumar, Devendra; Sakthivel, Rathinasamy; Nguyen Hoang Luc; Can, N. H.; Luc, Nguyen Hoang
    In this paper, we consider an inverse source problem for the time-space-fractional diffusion equation. Here, in the sense of Hadamard, we prove that the problem is severely ill-posed. By applying the quasi-reversibility regularization method, we propose by this method to solve the problem (1.1). After that, we give an error estimate between the sought solution and regularized solution under a prior parameter choice rule and a posterior parameter choice rule, respectively. Finally, we present a numerical example to find that the proposed method works well.
  • Article
    Citation - WoS: 20
    Citation - Scopus: 24
    Inverse Source Problem for Time Fractional Diffusion Equation With Mittag-Leffler Kernel
    (Springer, 2020) Nguyen Hoang Luc; Baleanu, Dumitru; Zhou, Yong; Le Dinh Long; Nguyen Huu Can; Long, Le Dinh; Can, Nguyen Huu; Luc, Nguyen Hoang
    In this work, we study the problem to identify an unknown source term for the Atangana-Baleanu fractional derivative. In general, the problem is severely ill-posed in the sense of Hadamard. We have applied the generalized Tikhonov method to regularize the instable solution of the problem. In the theoretical result, we show the error estimate between the regularized and exact solutions with a priori parameter choice rules. We present a numerical example to illustrate the theoretical result. According to this example, we show that the proposed regularization method is converged.
  • Article
    Citation - WoS: 19
    Citation - Scopus: 24
    Identifying the Space Source Term Problem for a Generalization of the Fractional Diffusion Equation With Hyper-Bessel Operator
    (Springer, 2020) Le Nhat Huynh; Baleanu, Dumitru; Nguyen Huu Can; Nguyen Hoang Luc; Huynh, Le Nhat; Luc, Nguyen Hoang; Can, Nguyen Huu
    In this paper, we consider an inverse problem of identifying the source term for a generalization of the time-fractional diffusion equation, where regularized hyper-Bessel operator is used instead of the time derivative. First, we investigate the existence of our source term; the conditional stability for the inverse source problem is also investigated. Then, we show that the backward problem is ill-posed; the fractional Landweber method and the fractional Tikhonov method are used to deal with this inverse problem, and the regularized solution is also obtained. We present convergence rates for the regularized solution to the exact solution by using an a priori regularization parameter choice rule and an a posteriori parameter choice rule. Finally, we present a numerical example to illustrate the proposed method.
  • Article
    Citation - WoS: 5
    Citation - Scopus: 5
    A Filter Method for Inverse Nonlinear Sideways Heat Equation
    (Springer, 2020) O'Regan, Donal; Baleanu, Dumitru; Nguyen Hoang Luc; Nguyen Can; Nguyen Anh Triet; Anh Triet, Nguyen; O’Regan, Donal; Hoang Luc, Nguyen; Luc, Nguyen Hoang; Can, Nguyen; Triet, Nguyen Anh
    In this paper, we study a sideways heat equation with a nonlinear source in a bounded domain, in which the Cauchy data at x=X are given and the solution in 0 <= x < X is sought. The problem is severely ill-posed in the sense of Hadamard. Based on the fundamental solution to the sideways heat equation, we propose to solve this problem by the filter method of degree alpha, which generates a well-posed integral equation. Moreover, we show that its solution converges to the exact solution uniformly and strongly in L-p(omega,X; L-2 (R)); omega is an element of[0,X) under a priori assumptions on the exact solution. The proposed regularized method is illustrated by numerical results in the final section.