On a time fractional diffusion with nonlocal in time conditions
Nguyen Hoang TuanDivision of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, VietnamNguyen Anh TrietDivision of Applied Mathematics, Thu Dau Mot University, Binh Duong Province, VietnamNguyen Hoang LucDivision of Applied Mathematics, Thu Dau Mot University, Binh Duong Province, VietnamNguyen Duc PhuongFaculty of Fundamental Science, Industrial University of Ho Chi Minh City, Ho Chi Minh City, Vietnam
2021en
ABI
Аннотация
Abstract In this work, we consider a fractional diffusion equation with nonlocal integral condition. We give a form of the mild solution under the expression of Fourier series which contains some Mittag-Leffler functions. We present two new results. Firstly, we show the well-posedness and regularity for our problem. Secondly, we show the ill-posedness of our problem in the sense of Hadamard. Using the Fourier truncation method, we construct a regularized solution and present the convergence rate between the regularized and exact solutions.
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