Identification of a time‐dependent coefficient in a partial differential equation subject to an extra measurement

The problem of recovering a time-dependent coefficient in a parabolic partial differential equation has attracted considerable recent attention. Several finite difference schemes are presented for identifying the function u(x, t) and the unknown coefficient a(t) in a one-dimensional partial differential equation. These schemes are developed to determine the unknown properties in a region by measuring only data on the boundary. Our goal has been focused on coefficients that presents physical quantities, for example, the conductivity of a medium. For the convenience of discussion, we will present the results of numerical experiment on several test problems. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005

[1]  B. Jones.  Various methods for finding unknown coefficients in parabolic differential equations , 1963 .

[2]  J. Cannon.  Determination of an unknown coefficient in a parabolic differential equation , 1963 .

[3]  Afet Golayoglu Fatullayev.  Numerical procedure for the determination of an unknown coefficients in parabolic equations , 2002 .

[4]  Mehdi Dehghan.  Determination of a control function in three-dimensional parabolic equations , 2003, Math. Comput. Simul..

[5]  William Rundell,et al.  Recovering a time dependent coefficient in a parabolic differential equation , 1991 .

[6]  John A. MacBain,et al.  Existence and uniqueness properties for the one‐dimensional magnetotellurics inversion problem , 1986 .

[7]  J. R. Cannon,et al.  Parameter determination in parabolic partial differential equations from overspecified boundary data , 1982 .

[8]  William Rundell,et al.  Determination of an unknown non-homogeneous term in a linear partial differential equation .from overspecified boundary data , 1980 .

[9]  John R. Cannon,et al.  On a class of nonlinear parabolic equations with nonlinear trace type functionals , 1991 .

[10]  Mehdi Dehghan.  New schemes for a two-dimensional inverse problem with temperature overspecification. , 2001 .

[11]  Yanping Lin,et al.  An inverse problem of finding a parameter in a semi-linear heat equation , 1990 .

[12]  Yanping Lin,et al.  A finite-difference solution to an inverse problem for determining a control function in a parabolic partial differential equation , 1989 .

[13]  Yanping Lin,et al.  Determination of source parameter in parabolic equations , 1992 .

[14]  Yanping Lin,et al.  Numerical procedures for the determination of an unknown coefficient in semi-linear parabolic differential equations , 1994 .

[15]  R. F. Warming,et al.  The modified equation approach to the stability and accuracy analysis of finite-difference methods , 1974 .

[16]  G. Pinder,et al.  Numerical solution of partial differential equations in science and engineering , 1982 .

[17]  Yanping Lin,et al.  Analytical and numerical solutions for a class of nonlocal nonlinear parabolic differential equations , 1994 .