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Nguyen Huy Tuan, Tran Thanh Binh, Tran Quoc Viet, Daniel Lesnic; On the Cauchy problem for semilinear elliptic equations; Journal of Inverse and Ill-posed Problems, Vol. 24, pp. 123 – 138.

Abstract

We study the Cauchy problem for nonlinear (semilinear) elliptic partial differential equations in Hilbert spaces. The problem is severely ill-posed in the sense of Hadamard. Under a weak a priori assumption on the exact solution, we propose a new regularization method for stabilising the ill-posed problem. These new results extend some earlier works on Cauchy problems for nonlinear elliptic equations. Numerical results are presented and discussed.

 
Keywords: Cauchy problem; nonlinear elliptic equation; ill-posed problem; error estimates