Các bài báo công bố quốc tế

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.


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