An Inverse Problem for Parabolic Partial Differential Equations with Nonlinear Conductivity Term
We consider an inverse problem for partial differential equation with nonlinear conductivity term in one-dimensional space within a finite interval. In the considered problem, a temperature history is unknown in a boundary of domain. The homotopy perturbation technique is used. Moreover, we have presented a numerical example.
J. V. Beck, B. Blackwell, and C. J. St. Clair, Jr., Inverse Heat Conduction: Ill-Posed Problems, John Willey & Sons, New York, NY, USA, 1985.
O. M. Alifonov, Inverse Heat Transfer Problems, Springer, Berlin, Germany, 1994.
M. N. Özisik and H. R. B. Orlande, Inverse Heat Transfer: Fundamentals and Applications, Taylor & Francis, New York, NY, USA, 2000.
J. R. Cannon, The One-Dimensional Heat Equation, Addison-Wesley, New York, NY, USA, 1984.
A. Shidfar and A. Zakeri, “A numerical method for backward inverse heat conduction problem with two unknown functions,” International Journal of Engineering Science, vol. 304, no. 16, pp. 71–74, 2008.View at: Google Scholar
A. Shidfar and A. Zakeri, “Asymptotic solution for an inverse parabolic problem,” Mathematica Balkanica, vol. 18, no. 3-4, pp. 475–483, 2004.View at: Google Scholar
A. Zakeri, Q. Jannati, and A. Aminataei, “Application of He's homotopy perturbation method for Cauchy problem in one-dimensional nonlinear equation of diffusion,” to appeare in International Journal of Engineering Science.View at: Google Scholar
J.-H. He, “Recent development of the homotopy perturbation method,” Topological Methods in Nonlinear Analysis, vol. 31, no. 2, pp. 205–209, 2008.View at: Google Scholar
J. R. Munkres, Topology, Prentice-Hall, Upper Saddle River, NJ, USA, 2nd edition, 2000.
D. D. Ganji and A. Sadighi, “Application of He's homotopy-perturbation method to nonlinear coupled systems of reaction-diffusion equations,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 7, no. 4, pp. 411–418, 2006.View at: Google Scholar