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“…Example 4. We take the boundary conditions, initial condition, and additional specification function (3)-(6) as [14,15] ( ) = ,…”

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“…Example 4. We take the boundary conditions, initial condition, and additional specification function (3)-(6) as [14,15] ( ) = ,…”

“…There are various numerical methods to solve (1) and (3)-(6) or similar problems. Deng et al [14] applied the gradient iteration algorithm for obtaining the approximate solutions. Kansa method is used by [15] to solve problem (1) and (2) and the stable experiments are given.…”

“…But an inevitable reality is that the inverse problem of identifying the coefficients in parabolic equations is often ill-posed, which leads to many difficulties on the study of the original inverse problem. For a helpful conversion from the original inverse problem to a tractable one, optimal control methods have been accepted by increasing researchers recently (for a survey of the studies see, for example [7][8][9][10][11][12]). Here, we mostly recall the studies of inverse problems on reaction-diffusion equations to state our main motivation in the study from the aspect of theory research.…”

“…A lot of research work has been carried out in recent years; see, for example, [3,6,7,10,11,14,[19][20][21][22] and the references therein. However, this method may over-smooth the exact solution, it cannot effectively approximate the original solution when the exact solution has some singularities.…”