Related papers: Nonlinear and Linearised Primal and Dual Initial B…
Estimation of the degree of stability and the bounds of solutions to non-autonomous nonlinear systems present major concerns in numerous applied problems. Yet, current techniques are frequently yield overconservative conditions which are…
Time-dependent models of fluid motion in thin layers, subject to signed source terms, represent important sub-problems within climate dynamics. Examples include ice sheets, sea ice, and even shallow oceans and lakes. We address these…
Mathematical modeling of many physical processes such as diffusion, viscosity of fluids and combustion involves differential equations with small coefficients of higher derivatives. These may be small diffusion coefficients for modeling the…
The null-timelike initial-boundary value problem for a hyperbolic system of equations consists of the evolution of data given on an initial characteristic surface and on a timelike worldtube to produce a solution in the exterior of the…
We study initial boundary value problems for linear scalar partial differential equations with constant coefficients, with spatial derivatives of {\em arbitrary order}, posed on the domain $\{t>0, 0<x<L\}$. We first show that by analysing…
In this paper, the initial and boundary problem of the difference equation which is a discretization of the semi-linear heat equation. The difference equation derived by discretizing the semi-linear heat equation has solutions which show…
We establish well-posedness of initial-boundary value problems for continuity equations with BV (bounded total variation) coefficients. We do not prescribe any condition on the orientation of the coefficients at the boundary of the domain.…
The identification of a linear system model from data has wide applications in control theory. The existing work that provides finite sample guarantees for linear system identification typically uses data from a single long system…
The Allen-Cahn equation, coupled with dynamic boundary conditions, has recently received a good deal of attention. The new issue of this paper is the setting of a rather general mass constraint which may involve either the solution inside…
We discuss initial-boundary value problems of arbitrary spatial order subject to arbitrary boundary conditions. We formalise the concept of the conditioning of such a problem and show that it represents a necessary criterion for…
In this paper, the discretization of a nonlinear wave equation whose nonlinear term is a power function is introduced. The difference equation derived by discretizing the nonlinear wave equation has solutions which show characteristics…
We discuss error identities for two classes of free boundary problems generated by obstacles. The identities suggest true forms of the respective error measures which consist of two parts: standard energy norm and a certain nonlinear…
Assessment of the degree of boundedness/stability of multidimensional nonlinear systems with time-dependent and nonperiodic coefficients is an important problem in various applied areas which has no adequate resolution yet. Most of the…
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.…
Motivated by an analysis on the well-posedness of the initial boundary value problem for the motion of an inextensible hanging string, we first consider an initial boundary value problem for one-dimensional degenerate hyperbolic systems…
In this paper we address the temporal energy growth associated with numerical approximations of the perfectly matched layer (PML) for Maxwell's equations in first order form. In the literature, several studies have shown that a numerical…
We study linear damped and viscoelastic wave equations evolving on a bounded domain. For both models, we assume that waves are subject to an inhomogeneous Neumann boundary condition on a portion of the domain's boundary. The analysis of…
We focus on the initial boundary value problem for a general scalar balance law in one space dimension. Under rather general assumptions on the flux and source functions, we prove the well-posedness of this problem and the stability of its…
The initial value problem is introduced after a thorough review of the essential geometry. The initial value equations are put into elliptic form using both conformal transformations and a treatment of the extrinsic curvature introduced…
Regularization and interior point approaches offer valuable perspectives to address constrained nonlinear optimization problems in view of control applications. This paper discusses the interactions between these techniques and proposes an…