Related papers: On one method of boundary value problem regulariza…
In this paper, we analyze nonlinear differential equations subject to generalized boundary conditions. More specifically, we provide a framework from which we can provide conditions, which are straightforward to check, for the solvability…
We examine two central regularization strategies for monotone variational inequalities, the first a direct regularization of the operative monotone mapping, and the second via regularization of the associated dual gap function. A key link…
The minimum value function appearing in Tikhonov regularization technique is very useful in determining the regularization parameter, both theoretically and numerically. In this paper, we discuss the properties of the minimum value…
We present a variational framework for studying the existence and regularity of solutions to elliptic free boundary problems that do not necessarily minimize energy. As applications, we obtain mountain pass solutions of critical and…
The paper considers a boundary value problem for the high-order Lavrent'ev-Bitsadze equation. Necessary and sufficient conditions for the uniqueness of the solution are found. When substantiating the existence, the problem of "small…
A Dirichlet-type problem is studied for an equation of even order with variable coefficients. A criterion for the uniqueness of a solution is given. The solution is built in the form of a Fourier series. When justifying the convergence of…
This note is concerned with the study of the initial boundary value problem for systems of conservation laws from the point of view of control theory, where the initial data is fixed and the boundary data are regarded as control functions.…
In this paper we consider a class of boundary value problems for third order nonlinear functional differential equation. By the reduction of the problem to operator equation we establish the existence and uniqueness of solution and…
We use convex relaxation techniques to provide a sequence of solutions to the matrix completion problem. Using the nuclear norm as a regularizer, we provide simple and very efficient algorithms for minimizing the reconstruction error…
The weak form of the SDOF and MDOF equations of motion are obtained. The original initial conditions problem is transformed into a boundary value problem. The boundary value problem is then solved and transformed back to the initial…
We prove conditions for existence of analytical solutions for boundary value problems with the Hilfer fractional derivative, generalizing the commonly used Riemann-Liouville and Caputo operators. The boundary values, referred to in this…
Overdetermined systems of first kind integral equations appear in many applications. When the right-hand side is discretized, the resulting finite-data problem is ill-posed and admits infinitely many solutions. We propose a numerical method…
Many systems of interest in cryptography consist of equations of the same degree. Under the assumption that the degree of regularity is finite, we prove upper bounds on the degree of regularity of a system of equations of the same degree,…
In this article I will review some basic results on elliptic boundary value problems with applications to General Relativity.
A general formula is presented for any order derivative of Chebyshev polynomials instead of the existing recursive relationship. Hence, the Chebyshev finite difference method is made applicable not only to second order problems but also to…
This paper presents adaptive boundary element methods for positive, negative, as well as zero order operator equations, together with proofs that they converge at certain rates. The convergence rates are quasi-optimal in a certain sense…
Nonlinear boundary value problems (BVPs) by means of the classical Lie symmetry method are studied. A new definition of Lie invariance for BVPs is proposed by the generalization of existing those on much wider class of BVPs. A class of…
The numerical solution of linear discrete ill-posed problems typically requires regularization, i.e., replacement of the available ill-conditioned problem by a nearby better conditioned one. The most popular regularization methods for…
Variational methods are employed in situations where exact Bayesian inference becomes intractable due to the difficulty in performing certain integrals. Typically, variational methods postulate a tractable posterior and formulate a lower…
In many astronomical problems one often needs to determine the upper and/or lower boundary of a given data set. An automatic and objective approach consists in fitting the data using a generalised least-squares method, where the function to…