Inverse problems for heat equation and space–time fractional diffusion equation with one measurement
نویسندگان
چکیده
منابع مشابه
On the Inverse Problem for a Fractional Diffusion Equation
We consider the inverse problem of finding the temperature distribution and the heat source whenever the temperatures at the initial time and the final time are given. The problem considered is one dimensional and the unknown heat source is supposed to be space dependent only. The existence and uniqueness results are proved.
متن کاملExistence and uniqueness in an inverse source problem for a one-dimensional time-fractional diffusion equation
In this study, an inverse source problem for a one-dimensional timefractional diffusion equation is considered. An existence theorem based on the minimization of an error functional between the output data and the additional data is proved. Then it is showed that the unknown source function can be determined uniquely by an additional data u(0, t), 0 ≤ t ≤ T using an auxiliary uniqueness result ...
متن کاملHarmonic Moments and an Inverse Problems for the Heat Equation
The paper is devoted to the solution of the inverse boundary problem for the heat equation. Let Ω be a connected bounded domain in R n (n ≥ 2) with C l (l ≥ 2) boundary Γ. Consider the mixed problem for the heat equation (1.1) (ρ(x)∂ t − −)u f (t, x) = 0 in (0, +∞) × Ω, u f (t, x) = f (t, x) o n(0 , +∞) × Γ, u f (0, x) = 0 on Ω. The density ρ(x) is a C l+σ , 0 < σ < 1, function on...
متن کاملFinite integration method with RBFs for solving time-fractional convection-diffusion equation with variable coefficients
In this paper, a modification of finite integration method (FIM) is combined with the radial basis function (RBF) method to solve a time-fractional convection-diffusion equation with variable coefficients. The FIM transforms partial differential equations into integral equations and this creates some constants of integration. Unlike the usual FIM, the proposed method computes constants of integ...
متن کاملUnified Fractional Kinetic Equation and a Fractional Diffusion Equation
Abstract. In earlier papers Saxena et al. (2002, 2003) derived the solutions of a number of fractional kinetic equations in terms of generalized Mittag-Leffler functions which extended the work of Haubold and Mathai (2000). The object of the present paper is to investigate the solution of a unified form of fractional kinetic equation in which the free term contains any integrable function f(t),...
متن کاملذخیره 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: Journal of Differential Equations
سال: 2020
ISSN: 0022-0396
DOI: 10.1016/j.jde.2020.05.022