Related papers: A random regularized approximate solution of the i…
We propose a regularization method to solve a nonlinear ill-posed problem connected to inversion of data gathered by a ground conductivity meter.
This paper studies the 1D pressureless turbulence (the Burgers equation). It shows that reliable numerics in this problem is very easy to produce if one properly discretizes the Burgers equation. The numerics it presents confirms the 7/2…
The article focuses on error estimates as well as stability analysis of deep learning methods for stationary and non-stationary viscous Burgers equation in two and three dimensions. The local well-posedness of homogeneous boundary value…
We obtain precise large time asymptotics for the Cauchy problem for Burgers type equations satisfying shock profile condition. The proofs are based on the exact a priori estimates for (local) solutions of these equations and a recent result…
This paper considers the inversion of ill-posed linear operators. To regularise the problem the solution is enforced to lie in a non-convex subset. Theoretical properties for the stable inversion are derived and an iterative algorithm akin…
We present a reduced basis offline/online procedure for viscous Burgers initial boundary value problem, enabling efficient approximate computation of the solutions of this equation for parametrized viscosity and initial and boundary value…
We present a regularization method to approach a solution of the pessimistic formulation of ill -posed bilevel problems . This allows to overcome the difficulty arising from the non uniqueness of the lower level problems solutions and…
We develop ergodic theory of the inviscid Burgers equation with random kick forcing in noncompact setting. The results are parallel to those in our recent work on the Burgers equation with Poissonian forcing. However, the analysis based on…
We introduce in this document a direct method allowing to solve numerically inverse type problems for linear hyperbolic equations. We first consider the reconstruction of the full solution of the wave equation posed in $\Omega\times (0,T)$…
When solving rank-deficient or discrete ill-posed problems by regularization methods, the choice of the regularization parameter is crucial. It is also of interest, the regularization norm used in the selection of the solution. In this…
A detailed analysis of the invariant point transformations for the first four partial differential equations which belong to the Complex Burgers` Hierarchy is performed. Moreover, a detailed application of the reduction process through the…
We construct solutions to Burgers type equations perturbed by a multiplicative space-time white noise in one space dimension. Due to the roughness of the driving noise, solutions are not regular enough to be amenable to classical methods.…
Conditional stability estimates require additional regularization for obtaining stable approximate solutions if the validity area of such estimates is not completely known. In this context, we consider ill-posed nonlinear inverse problems…
In this article we investigate an inexact iterative regularization method based on generalized Bregman distances of an optimal control problem with control constraints. We show robustness and convergence of the inexact Bregman method under…
For ill-posed inverse problems, a regularised solution can be interpreted as a mode of the posterior distribution in a Bayesian framework. This framework enriches the set the solutions, as other posterior estimates can be used as a solution…
We introduce a new concepts of weak solution for the conservative stochastic Burgers equation in any dimension. The definition is based on weak solution concepts introduced by various authors in order to make sense of equations which do not…
Regularization methods are a key tool in the solution of inverse problems. They are used to introduce prior knowledge and make the approximation of ill-posed (pseudo-)inverses feasible. In the last two decades interest has shifted from…
The numerical approximation of an inverse problem subject to the convection--diffusion equation when diffusion dominates is studied. We derive Carleman estimates that are on a form suitable for use in numerical analysis and with explicit…
We study an iterative regularization method of optimal control problems with control constraints. The regularization method is based on generalized Bregman distances. We provide convergence results under a combination of a source condition…
This paper provides a new regularization method which is particularly suitable for linear exponentially ill-posed problems. Under logarithmic source conditions (which have a natural interpretation in terms of Sobolev spaces in the…