# A note on the stability of a time-dependent source identification problem

## Related Articles

- An inverse problem of identifying the radiative coefficient in a degenerate parabolic equation. Deng, Zuicha; Yang, Liu // Chinese Annals of Mathematics;May2014, Vol. 35 Issue 3, p355
The authors investigate an inverse problem of determining the radiative coefficient in a degenerate parabolic equation from the final overspecified data. Being different from other inverse coefficient problems in which the principle coefficients are assumed to be strictly positive definite, the...

- Inverse problem of finding n coefficients of lower derivatives in a parabolic equation. Kamynin, V.; Kostin, A. // Differential Equations;Apr2014, Vol. 50 Issue 4, p476
We consider the problem of reconstructing the vector function $\vec b(x) = (b_1 ,...,b_n )$ in the term $(\vec b,\nabla u)$ in a linear parabolic equation. This coefficient inverse problem is considered in a bounded domain Î© âŠ‚ R. To find the above-mentioned function $\vec b(x)$, in...

- On an over-determined problem of free boundary of a degenerate parabolic equation. Pan, Jiaqing // Applications of Mathematics;Dec2013, Vol. 58 Issue 6, p657
This work is concerned with the inverse problem of determining initial value of the Cauchy problem for a nonlinear diffusion process with an additional condition on free boundary. Considering the flow of water through a homogeneous isotropic rigid porous medium, we have such desire: for every...

- On the unique solvability of an inverse problem for a semilinear parabolic equation. Sazaklioglu, Ali Ugur; Erdogan, Abdullah Said // AIP Conference Proceedings;2015, Vol. 1676 Issue 1, p1
In the present paper, unique solvability of an inverse problem of source identification governed by a semilinear parabolic equation is investigated. Moreover, for the numerical solution of this problem finite difference method is applied. The convergence estimate for the solution of the...

- Inverse Problems for a Parabolic Integrodifferential Equation in a Convolutional Weak Form. Kasemets, Kairi; Janno, Jaan // Abstract & Applied Analysis;2013, p1
We deduce formulas for the FrÃ©chet derivatives of cost functionals of several inverse problems for a parabolic integro differential equation in a weak formulation. The method consists in the application of an integrated convolutional form of the weak problem and all computations are...

- On the solvability of the inverse problem for determining the right-hand side of a degenerate parabolic equation with integral observation. Kamynin, V. // Mathematical Notes;Nov2015, Vol. 98 Issue 5/6, p765
Existence and uniqueness theorems and theorems on stability under perturbations of the input data for solutions of the inverse problem for a degenerate parabolic equation in the plane with integral observation are obtained. The cases of bounded and unbounded coefficients are studied. Estimates...

- Nonlocal Inverse Problem for a Parabolic Equation with Degeneration. Huzyk, N. M. // Ukrainian Mathematical Journal;Nov2013, Vol. 65 Issue 6, p847
We establish conditions for the existence and uniqueness of a classical solution of the inverse problem of determination of the time-dependent coefficient of the higher-order derivative in a parabolic equation with degeneration in the coefficient of the time derivative. We impose boundary...

- Fractional-Order Controller Design for Oscillatory Fractional Time-Delay Systems Based on the Numerical Inverse Laplace Transform Algorithms. Liu, Lu; Pan, Feng; Xue, Dingyu // Mathematical Problems in Engineering;4/21/2015, Vol. 2015, p1
Fractional-order time-delay system is thought to be a kind of oscillatory complex system which could not be controlled efficaciously so far because it does not have an analytical solution when using inverse Laplace transform. In this paper, a type of fractional-order controller based on...

- EXPERIMENTAL VERIFICATION OF APPROXIMATE SOLUTION OF THE INVERSE STEFAN PROBLEM OBTAINED BY APPLYING THE INVASIVE WEED OPTIMIZATION ALGORITHM. HETMANIOK, Edyta; SLOTA, Damian; ZIELONKA, Adam // Thermal Science;2015 Supplement, Vol. 19, pS205
The paper proposes a procedure for solving the inverse Stefan problem consisted in reconstruction of the function describing the heat transfer coefficient on the basis of temperature measurements. Elaborated method is based on two procedures: solution of the appropriate direct Stefan problem by...