UNIQUENESS OF RECOVERY OF SOME QUASILINEAR PARTIAL DIFFERENTIAL EQUATIONS
Victor Isakov · Communications in Partial Differential Equations · 2001
We prove uniqueness of the term c(u,p) of partial differential equations −Δu + c(u, ∇u) = 0 and ∂ t u − Δu + c(u, ∇u) = 0 with the Dirichlet-to-Neumann map given on a part of the lateral boundary. We use a linearization method and singular solutions in the boundary reconstruction of the linearized equations