Abstract. A new parameter choice method for Tikhonov regularization of discrete ill-posed problems is presented. Some of the regularized solutions of a discrete ill-posed problem are less sensitive than others to the perturbations in the right-hand side vector. This method chooses one of the insensitive regularized solutions using a certain criterion. Numerical experiments show that the new met...

In this paper, we would like to briefly introduce some applications of fractional derivatives in the fields heat and fluid-flows. However, our main focus is on study an inverse source problem for Rayleigh-Stokes problem. The severely ill-posed. We verify ill-posedness Problem 1, applying modified Lavrentiev construct a regularization from exact data. After that, established convergent rate betw...

In many applications of solving ill-posed problems there are a number of regularization methods to choose from as well as a free regularization parameter. The choice of the method and regularization can add bias if deblurred images are based on what the researcher expects. The presented project develops a tool for method choice and parameter selection by using a set of three statistical diagnos...

In this paper, we consider in Rn the Cauchy problem for the nonlinear Schrödinger equation with initial data in the Sobolev space W s,p for p < 2. It is well known that this problem is ill posed. However, we show that after a linear transformation by the linear semigroup the problem becomes locally well posed in W s,p for 2n n+1 < p < 2 and s > n(1 − 1 p ). Moreover, we show that in one space d...

This paper deals with ill-posed bilevel programs, i.e., problems admitting multiple lower-level solutions for some upper-level parameters. Many publications have been devoted to the standard optimistic case of this problem, where the difficulty is essentially moved from the objective function to the feasible set. This new problem is simpler but there is no guaranty to obtain local optimal solut...

In this paper the description of the simplest variant of conservative averaging method for partial differential (or integro-differential) equations in cylinder type domain is given. Different types of boundary conditions (both linear and non-linear) are considered. As application of the method the process of intensive steel quenching as the time inverse ill-posed problem for the hyperbolic heat...

We study dispersive models of fluid flow in viscoelastic vessels, derived the blood flow. The unknowns are velocity axial direction and displacement vessel wall from rest. prove that one such model has a well-posed initial value problem, while we argue related instead an ill-posed problem; second case, still existence solutions analytic function spaces. Finally some periodic traveling waves.

Well-posedness of the Cauchy problem is analyzed for a singular Vlasov equation governing the evolution of the ionic distribution function of a quasineutral fusion plasma. The Penrose criterium is adapted to the linearized problem around a time and space homogeneous distribution function showing (due to the singularity) more drastic differences between stable and unstable situations. This patho...

‎in the present paper we consider a time-fractional inverse diffusion problem‎, ‎where data is given at $x=1$ and the solution is required in the interval $0

Blind system identification is known to be an ill-posed problem and without further assumptions, no unique solution is at hand. In this contribution, we are concerned with the task of identifying an ARX model from only output measurements. We phrase this as a constrained rank minimization problem and present a relaxed convex formulation to approximate its solution. To make the problem well pose...