Filtering Function Method for the Cauchy Problem of a Semi-Linear Elliptic Equation

Show more

References

[1] Kirsch, A. (1996) An Introduction to the Mathematical Theory of Inverse Problems. Applied Mathematical Sciences, Vol. 120, Springer-Verlag, New York.

http://dx.doi.org/10.1007/978-1-4612-5338-9

[2] Engl, H.W., Hanke, M. and Neubauer, A. (1996) Regularization of Inverse Problems. Mathematics and Its Applications, Vol. 375, Kluwer Academic Publishers Group, Dordrecht.

http://dx.doi.org/10.1007/978-94-009-1740-8

[3] Belgacem, F.B. (2007) Why Is the Cauchy Problem Severely Ill-Posed? Inverse Problems, 23, 823.

http://dx.doi.org/10.1088/0266-5611/23/2/020

[4] Feng, X.L., Ning, W.T. and Qian, Z. (2014) A Quasi-Boundary-Value Method for a Cauchy Problem of an Elliptic Equation in Multiple Dimensions. Inverse Problems in Science and Engineering, 22, 1045-1061.

http://dx.doi.org/10.1080/17415977.2013.850683

[5] Hào, D.N., Duc, N.V. and Lesnic, D. (2009) A Non-Local Boundary Value Problem Method for the Cauchy Problem for Elliptic Equations. Inverse Problems, 25, Article ID: 055002.

http://dx.doi.org/10.1088/0266-5611/25/5/055002

[6] Hào, D.N., Van, T.D. and Gorenflo, R. (1992) Towards the Cauchy Problem for the Laplace Equation. Partial Differential Equations, 111.

[7] Isakov, V. (2006) Inverse Problems for Partial Differential Equations. Springer Verlag, Berlin.

[8] Lavrentiev, M.M., Romanov, V.G. and Shishatski, S.P. (1986) Ill-Posed Problems of Mathematical Physics and Analysis. Translations of Mathematical Monographs, Vol. 64, American Mathematical Society, Providence.

[9] Zhang, H.W. and Wei, T. (2014) A Fourier Truncated Regularization Method for a Cauchy Problem of a Semi-Linear Elliptic Equation. Journal of Inverse and Ill-Posed Problems, 22, 143-168.

http://dx.doi.org/10.1515/jip-2011-0035

[10] Tuan, N.H., Thang, L.D. and Khoa, V.A. (2015) A Modified Integral Equation Method of the Nonlinear Elliptic Equation with Globally and Locally Lipschitz Source. Applied Mathematics and Computation, 265, 245-265.

http://dx.doi.org/10.1016/j.amc.2015.03.115

[11] Tuan, N.H. and Tran, B.T. (2014) A Regularization Method for the Elliptic Equation with Inhomogeneous Source. ISRN Mathematical Analysis, 2014, Article ID: 525636.

[12] Clark, G.W. and Oppenheimer, S.F. (1994) Quasireversibility Methods for Non-Well-Posed Problems. Electronic Journal of Differential Equations, 1994, 9 p.

[13] Xiong, X.T. (2010) A Regularization Method for a Cauchy Problem of the Helmholtz Equation. Journal of Computational and Applied Mathematics, 233, 1723-1732.

http://dx.doi.org/10.1016/j.cam.2009.09.001

[14] Tuan, N.H. and Trong, D.D. (2010) A Nonlinear Parabolic Equation Backward in Time: Regularization with New Error Estimates. Nonlinear Analysis: Theory, Methods and Applications, 73, 1842-1852.

[15] Evans, L.C. (1998) Partial Differential Equations. American Mathematical Society, Vol. 19.