This study is related to inverse coefficient problems for a nonlinear parabolic variational inequality with an unknown leading coefficient in the equation for the gradient of the solution. An inverse method, involving minimization of a least-squares cost functional, is developed to identify the unknown coefficient. It is proved that the solution of the corresponding direct problem depends conti...

We give some stability estimates for the inverse problem consisting in the determination of source term and coefficients which appear in an elliptic or parabolic equations and depend fully on all the components of variables, from boundary measurements.

We will show that the same type of estimates known for the fundamental solutions for scalar parabolic equations with smooth enough coefficients hold for the first order derivatives of fundamental solution with respect to space variables of scalar parabolic equations of divergence form with discontinuous coefficients. The estimate is very important for many applications. For example, it is impor...

A parabolic equation and, more generally, parabolic inequality is considered in the cylinder QT = Ω × (0, T ) , where Ω ⊂ Rn is a bounded domain. Cauchy data, i.e., both Dirichlet and Neumann data are given at the lateral surface ST = ∂Ω × (0, T ). Logarithmic stability estimates are obtained for the unknown initial condition at {t = 0}. These estimates enable one to establish convergence rate ...

We consider the inverse problem of identification degenerate diffusion coefficient form $x^\alpha a(x)$ in a one dimensional parabolic equation by some extra data. first prove energy methods uniqueness and Lipschitz stability results for constant $a$ power $\alpha$ knowing an interior data at time. On other hand, we obtain result general coefficients $a(x)$ also boundary on side space interval....