In the present paper, we investigate the dual regularized total least squares (dual RTLS) from a computational aspect. More precisely, we propose a strategy for finding two regularization parameters in the resulting equation of dual RTLS. This strategy is based on an extension of the idea of model function originally proposed by Kunisch, Ito and Zou for a realization of the discrepancy principl...

A discrete-time linear optimal control problem with given initial and terminal times, state-control constraints, and variable end points is set forth. Corresponding to this primal control problem, or maximization problem, is a dual linear control problem, or minimization problem. The fundamental properties of duality are stated. A dual maximum principle is proved with the aid of the duality the...

We prove the existence of at least two solutions for a fourth order equation, which includes the vortex equations for the U(1) and CP (1) self-dual Maxwell-Chern-Simons models as special cases. Our method is variational, and it relies on an “asymptotic maximum principle” property for a special class of supersolutions to this fourth order equation.

An abstract functional framework is developed for the dual Petrov-Galerkin formulation of the initial boundary value problems with a third-order spatial derivative. This framework is then applied to study the wellposedness and decay properties of Airy equation and KdV equation in a finite interval.

In this work, the triple convolution of Daubechies wavelet is used to solve the three dimensional (3D) microscale Dual Phase Lag (DPL) problem. Also, numerical solution of 3D time-dependent initial-boundary value problems of a microscopic heat equation is presented. To generate a 3D wavelet we used the triple convolution of a one dimensional wavelet. Using convolution we get a scaling function ...

A Hamilton-Jacobi equation involving a double obstacle problem is investigated. The link between this equation and the notion of dual solutions—introduced in [1, 2, 3] in the framework of differential games with lack of information—is established. As an application we characterize the convex hull of a function in the simplex as the unique solution of some nonlinear obstacle problem.

A master equation (n dimensional non–Abelian current conservation law with mutually commuting current components) is introduced for multi-dimensional non-linear field theories. It is shown that the master equation provides a systematic way to understand 2-d integrable non-linear equations as well as 4-d self-dual equations and, more importantly, their generalizations to higher dimensions.