Parameter determination in a parabolic inverse problem in general dimensions

[1] P. Amore, A variational Sinc collocation method for Strong-Coupling problems, Journal
of Physics A, 39 (22) (2006) 349-355.
[2] J.R. Cannon, Y. Lin, Determination of parameter p(t) in Holder classes for some semi-
linear parabolic equations, Inverse Problems 4, (1988) 595-606.

[3] J.R. Cannon, Y. Lin, An inverse problem of nding a parameter in a semi-linear heat
equation, Journal of Mathematical Analysis and Applications, 145(2) (1990) 470-484.
[4] J.R. Cannon, Y. Lin, S. Wang, Determination of source parameter in parabolic equa-
tions, Meccanica 27, (1992) 85-94.
[5] J.R. Cannon, Y. Lin, Determination of a parameter p(t) in some quasilinear parabolic
dierential equations, Inverse Problems 4, (1988) 35-45.
[6] J.R. Cannon, The one dimensional heat equation, 1984 (Reading, MA: Addison-Wesley).
[7] M. Dehghan, M. Tatari, Determination of a control parameter in a one-dimensional par-
abolic equation using the method of radial basis functions, Mathematical and Computer
Modelling 44, (2006) 1160-1168.
[8] M. Dehghan, An inverse problem of nding a source parameter in a semilinear parabolic
equation, Applied Mathematical Modelling 25, (2001) 743-754.
[9] M. Dehghan, A. Saadatmandi, A tau method for the one-dimensional parabolic inverse
problem subject to temperature overspecication, Computational Mathematics with Ap-
plications, 52 (2006) 933-940.
[10] M. Dehghan, Finding a control parameter in one-dimensional parabolic equations, Ap-
plied Mathematics and Computation, 135 (2003) 491-503.
[11] M. Dehghan, Numerical solution of one-dimensional parabolic inverse problem, Applied
Mathematics and Computation, 136 (2003) 333-344.
[12] M. Dehghan, Determination of a control function in three-dimensional parabolic equa-
tions, Mathematics and Computers in Simulation, 61 (2003) 89-100.
[13] M. Dehghan, Determination of a control parameter in the two-dimensional diusion
equation,Applied Numerical Mathematics, 37 (2001) 489-502.
[14] M. Dehghan, Fourth order techniques for identing a control parameter in the parabolic
equations, International Journal of Engineering Science, 40 (2002) 433-447.
[15] M. Dehghan, Method of lines solutions of the parabolic inverse problem with an over-
specication at apoint, Numerical Algorithms, 50 (2009) 417-437.
[16] M. Dehghan, Finite dierence schemes for two-dimensional parabolic inverse problem
with temperature overspecication, International Journal of Computer Mathematics,
75 (3) (2000) 339-349.
[17] F. Li, Z. Wu, Ch. Ye, A nite dierence solution to a two-dimensional parabolic inverse
problem,Applied Mathematical Modelling, 36 (2012) 2303-2313.
[18] Y. Lin, An inverse problem for a cleass of quasilinear parabolic equations, SIAM Journal
on Mathematical Analysis, 22(1) (1991) 146-156.
[19] J. Lund, K. Bowers, Sinc methods for quadrature and dierential equations,SIAM,
Philadelphia, 1992.
[20] J. Lund, C. Vogel, A Fully-Galerkin method for the solution of an inverse problem in a
parabolic partial dierential equation, Inverse Problems, 6 (1990) 205-217.
[21] A.I. Prilepko, D.G. Orlovskii, Determination of the evolution parameter of an equation
and inverse problems of mathematical physics, Part I. Journal of Dierential Equations,
21 (1985) 119-129 [and part II, 21 (1985) 694-701].
[22] A.I. Prilepko, V.V. Soloev, Solvability of the inverse boundary value problem of nd-
ing a coecient of a lower order term in a parabolic equation. Journal of Dierential
Equations, 23(1) (1987) 136-143.
[23] W. Rundell, Determination of an unknownnon-homogeneous term in a linear partial
dierential equation from overspecied boundary data, Applicable Analysis, 10 (1980)
231-242.

[24] A. Shidfar, R. Zolfaghari, J. Damirchi, Application of Sinc-collocation method for solv-
ing an inverse problem, Journal of Computational and Applied Mathematics, 233 (2009)
545-554.
[25] A. Shidfar, R. Zolfaghari, Determination of an unknown function in a parabolic in-
verse problem by Sinc-collocation method,Numerical Methods for Partial Dierential
Equations, 27 (6) (2011) 1584-1598.
[26] R. Smith, K. Bowers, A Sinc-Galerkin estimation of diusivity in parabolic problems,
Inverse Problems, 9 (1993).
[27] F. Stenger, Numerical methods based on Sinc and analytic functions, Springer, New
York, 1993.
[28] S. Wang, Y. Lin, A nite dierence solution to an invese problem determining a control
function in a parabolic partial dierential equation, Inverse Problems, 5 (1989) 631-640.
[29] S. A. Youse, M. Dehghan, Legendre multiscaling functions for solving the one-
dimensional parabolic inverse problem, Numerical Methods for Partial Dierential
Equations, 25 (2009) 1502-1510.