An existence and uniqueness theorem for one optimal control problem (Q1346390)

In this paper, the authors consider an optimal control problem for a quasilinear parabolic equation on the line with scalar (from \(\mathbb{R}^ N)\) controls. The problem of the continuous dependence of the cost functional on controls is discussed. The paper contains misprints, inexact formulations and improper proofs (the authors ignore the fact that the normal derivatives of the solution on the boundary demand a specific treatment).