We consider the solution to Burger’s equation coupled to a stochastic noise in Ito’s sense. The main random properties of the wave are determined. The solution is related to a deterministic problem with a rescaled diffusion coefficient. Depending on the value of a parameter, the initial value problem may be ill posed, well posed up to an explosion time, or well posed for all time. Traveling wav...

This paper investigates the problem posed by direct feedback in automata networks. Such a feedback introduces a direct instantaneous depending of the input of a system upon itself through a signal path within the network. In continuous system theory such a feedback yields an algebraic loop, which may render the overall system ill-posed. In discrete-event system theory this problem has not been ...

In this work, we analyze the behavior of the active-set method for the nonnegative regularization of discrete ill-posed problems. In many applications, the solution of a linear ill-posed problem is known to be nonnegative. Standard Tikhonov regularization often provides an approximated solution with negative entries. We apply the activeset method to find a nonnegative approximate solution of th...

Reconstructing the structure of soil using non-invasive techniques is a very relevant problem in many scientific fields, like geophysics and archaeology. This can be done, for instance, with aid Frequency Domain Electromagnetic (FDEM) induction devices. Inverting FDEM data challenging inverse problem, as extremely ill-posed, i.e., sensible to presence noise measured data, non-linear. Regulariza...

It has been shown recently that steady frictional sliding along an interface between dissimilar elastic solids with Coulomb friction acting at the interface is ill-posed for a wide range of material parameters and friction coefficients. The ill-posedness is manifest in the unstable growth of interfacial disturbances of all wavelengths, with growth rate inversely proportional to the wavelength. ...

In this paper, we consider the inverse problem for identifying initial value of time–space fractional nonlinear diffusion equation. The uniqueness solution is proved by taking fixed point theorem Banach compression, and ill-posedness analyzed through exact solution. quasi-boundary regularization method chosen to solve ill-posed problem, error estimate between given. Moreover, several numerical ...

We consider optimal control problems associated to generally non-well posed Cauchy in a general framework. Firstly, we approximate the ill-posed problem with family of well-posed one and show that solutions latter converge former one. Secondly, investigate minimization approximated state equation. prove existence uniqueness minimizers characterize optimality systems. Finally, subjected equation...

In this paper, we discuss the classical ill-posed problem of numerical differentiation, assuming that the smoothness of the function to be differentiated is unknown. Using recent results on adaptive regularization of general ill-posed problems, we propose new rules for the choice of the stepsize in the finite-difference methods, and for the regularization parameter choice in numerical different...

Many popular solution methods for large discrete ill-posed problems are based on Tikhonov regularization and compute a partial Lanczos bidiagonalization of the matrix. The computational effort required by these methods is not reduced significantly when the matrix of the discrete ill-posed problem, rather than being a general nonsymmetric matrix, is symmetric and possibly indefinite. This paper ...

The numerical solution of linear discrete ill-posed problems typically requires regularization. Two of the most popular regularization methods are due to Tikhonov and Lavrentiev. These methods require the choice of a regularization matrix. Common choices include the identity matrix and finite difference approximations of a derivative operator. It is the purpose of the present paper to explore t...