We investigate the ill-posed inverse problem of recovering unknown spatially dependent
parameters in nonlinear evolution partial differential equations (PDEs). We propose a bi …

We develop a parallel two-level domain decomposition method for the 3D unsteady source
identification problem governed by a parabolic partial differential equation (PDE). The …

In this paper, we consider the inverse source problem for the time-fractional diffusion
equation, which has been known to be an ill-posed problem. To deal with the ill-posedness …

This work is devoted to an inverse problem of identifying a source term depending on both
spatial and time variables in a parabolic equation from single Cauchy data on a part of the …

We consider an optimal control problem governed by a one-dimensional elliptic equation
that involves univariate functions of bounded variation as controls. For the discretization of …

In this paper, we consider an inverse space-dependent source problem for a time-fractional
diffusion equation. To deal with the ill-posedness of the problem, we transform the problem …

The first being a parabolic optimal control problem governed by space-time measure
controls. This problem has a nice sparsity structure, which motivates our aim to achieve …

Optimal control of differential equations is concerned with finding “controls”(ie, inputs such
as right-hand sides, boundary conditions, coefficients, or domains) to differential equations …

We consider optimal control of an elliptic two-point boundary value problem governed by
functions of bounded variation (BV). The cost functional is composed of a tracking term for …

Several engineering problems result in a PDE-constrained optimization problem that aims at
finding the shape of a solid inside a fluid which minimizes a given cost function. These …