An asymptotic regularization method for coefficient identification of a generalized nonhomogeneous Helmholtz equation (Q1922265)

We consider the problem of coefficient identification for the generalized nonhomogeneous the Helmholtz equation \[ - \text{div} (a\nabla u)- bu= f\quad \text{in}\quad \Omega,\quad u- g\in H^1_0(\Omega),\tag{1} \] where \(\Omega\subset \mathbb{R}^N\) is a bounded domain with Lipschitz boundary \(\partial\Omega\). We use an asymptotic regularization technique for the approximation of the nonnegative coefficients \(a\) and \(b\), given the data \(f\), \(g\) and a solution \(u\) of problem (1).