Recovering a Space-Dependent Source Term in the Fractional Diffusion Equation with the Riemann–Liouville Derivative

نویسندگان

چکیده

This research determines an unknown source term in the fractional diffusion equation with Riemann–Liouville derivative. problem is ill-posed. Conditional stability for inverse can be given. Further, a Tikhonov regularization method was applied to regularize problem. In theoretical results, we propose priori and posteriori parameter choice rules obtain convergence estimates.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Finite Element Solutions for the Space Fractional Diffusion Equation with a Nonlinear Source Term

and Applied Analysis 3 Baeumer et al. 8, 13 have proved existence and uniqueness of a strong solution for 1.2 using the semigroup theory when f x, t, u is globally Lipschitz continuous. Furthermore, when f x, t, u is locally Lipschitz continuous, existence of a unique strong solution has also been shown by introducing the cut-off function. Finite difference methods have been studied in 14–16 fo...

متن کامل

Simultaneous Inversion for Space-Dependent Diffusion Coefficient and Source Magnitude in the Time Fractional Diffusion Equation

We deal with an inverse problem of simultaneously identifying the space-dependent diffusion coefficient and the source magnitude in the time fractional diffusion equation from viewpoint of numerics. Such simultaneous inversion problem is often of severe ill-posedness as compared with that of determining a single coefficient function. The forward problem is solved by employing an implicit finite...

متن کامل

Symmetries and exact solutions of the time fractional Harry-Dym equation with RiemannLiouville derivative

In this paper, group analysis of the time fractional Harry-Dym equation with Riemann– Liouville derivative is performed. Its maximal symmetry group in Lie’s sense and the corresponding optimal system of subgroups are determined. Similarity reductions of the equationunder study are performed. As a result, the reduced fractional ordinary differential equations are deduced, and some group invarian...

متن کامل

Landweber iterative method for identifying a space-dependent source for the time-fractional diffusion equation

*Correspondence: [email protected] School of Science, Lanzhou University of Technology, Lanzhou, Gansu 730050, P.R. China Abstract This paper is devoted to identifying an unknown source for a time-fractional diffusion equation with variable coefficients in a general bounded domain. This is an ill-posed problem. Firstly, we obtain a regularization solution by the Landweber iterative regularizatio...

متن کامل

Linear Space-time Fractional Reaction-diffusion Equation with Composite Fractional Derivative in Time

In this paper, we consider linear space-time fractional reactiondiffusion equation with composite fractional derivative as time derivative and Riesz-Feller fractional derivative with skewness zero as space derivative. We apply Laplace and Fourier transforms to obtain its solution.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Mathematics

سال: 2022

ISSN: ['2227-7390']

DOI: https://doi.org/10.3390/math10173213