An inverse problem for a nonlinear diffusion equation

Using empirical Eigenfunctions and Galerkin method to two‐phase transport models

“…In general, inverse problems are difficult to solve. These problems have been discussed in the literature by many authors such as Canon [18], Beck [19], and Shidfar [20][21][22]. Here, to solve the inverse problem we use the POD-Galerkin method proposed in section 3, which provides fast and accurate solutions.…”

A method for solving an inverse biharmonic problem

“…By demonstrating the following result, we will identify the function D(ω), when (D(ω), ω) is a solution to the inverse problem (1)- (5). For this purpose, we consider some methods introduced by Cannon [2], Matsuzawa [1], DuChateau [18], Shidfar [5,10], and Rundell [6,7].…”

“…For this purpose, we consider some methods introduced by Cannon [2], Matsuzawa [1], DuChateau [18], Shidfar [5,10], and Rundell [6,7]. Now, let us purpose M(x, y) = div(D(ω) grad ω), then equivalently, we have to couple systems of problems…”

“…In the next section, we consider the inverse problem (1)-(5), and describes some existence and uniqueness results for the solution pair (D(ω), ω) satisfying (1)- (5). The coefficient D(ω) will be determine in terms of q, f , f 1 , f 2 , and f 3 .…”

Estimation of concentration-dependent diffusion coefficient in drying process from the space-averaged concentration versus time with experimental data

“…Nonlinear inverse problems have drawn the attention of many researchers and have been previously treated by many authors (Alifanov, 1994;Alifanov et al, 1995;Fatullayev, 2001;Cannon and Duchateau, 1978;Shifdar and Azary, 1997;Muzylev, 1986). Mathematically, the inverse coefficient problems belong to the class of "ill-posed problems" that is the solution should satisfy the following requirements: existence, uniqueness, and stability with respect to the inherent present errors in the measurements.…”