An analytical solution for the nonlinear inverse Cauchy problem

Abdeljalil Nachaoui (1) , Hero W. Salih

1 LMJL - Laboratoire de Mathématiques Jean Leray

This paper discusses the recovering of both Dirichlet and Neumann data on some part of the domain boundary, starting from the knowledge of these data on another part of the boundary for a family of quasi-linear inverse problems. The nonlinear problem is reduced to a linear Cauchy problem for the Laplace equation coupled with a sequence of nonlinear scalar equations. We solve the linear problem using a closed-form regularization analytical solution. Various numerical examples and effects of added small perturbations into the input data are investigated. The numerical results show that the method produces a stable reasonably approximate solution

Mots clés: Nonlinear inverse problems; Cauchy problem; analytical regularization solution

Domaines: Mathématiques [math]; Analyse numérique [math.NA]

Abdeljalil Nachaoui, Hero W. Salih. An analytical solution for the nonlinear inverse Cauchy problem. Advanced Mathematical Models & Applications, 2021, 6 (3), pp.191-205. ⟨hal-03508117⟩