Related papers: Well-posed two-point initial-boundary value proble…
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…
We examine the analytic extension of solutions of linear, constant-coefficient initial-boundary value problems outside their spatial domain of definition. We use the Unified Transform Method or Method of Fokas, which gives a representation…
We derive the solution representation for a large class of nonlocal boundary value problems for linear evolution PDEs with constant coefficients in one space variable. The prototypical such PDE is the heat equation, for which problems of…
We provide a formulation of the initial boundary value problem for Friedrich's extended conformal Einstein field equations in which boundary data is prescribed on a timelike hypersurface located at a finite position in the spacetime. Our…
The initial-boundary value problems for linear non-autonomous first order evolution equations are examined. Our assumptions provide a unified treatment which is applicable to many situations, where the domains of the operators may change…
A well-posed initial-boundary value problem is formulated for the model problem of the vector wave equation subject to the divergence-free constraint. Existence, uniqueness and stability of the solution is proved by reduction to a system…
These lecture notes accompany two classes given at the NRHEP2 school. In the first lecture I introduce the basic concepts used for analyzing well-posedness, that is the existence of a unique solution depending continuously on given data, of…
A new method for the solution of initial-boundary value problems for evolution PDEs recently introduced by Fokas is generalised to multidimensions. Also the relation of this method with the method of images and with the classical integral…
We study the well-posedness for initial boundary value problems associated with time fractional diffusion equations with non-homogenous boundary and initial values. We consider both weak and strong solutions for the problems. For weak…
We consider the initial boundary value problem for free-evolution formulations of general relativity coupled to a parametrized family of coordinate conditions that includes both the moving puncture and harmonic gauges. We concentrate…
In this short communication, we announce an algorithmic procedure for constructing non-uniqueness counter-examples of classical solutions to initial-boundary-value problems for a wide class of linear evolution partial differential…
We present the numerical solution of two-point boundary value problems for a third order linear PDE, representing a linear evolution in one space dimension. The difficulty of this problem is in the numerical imposition of the boundary…
We study the local and global wellposedness of the initial-boundary value problem for the biharmonic Schr\"odinger equation on the half-line with inhomogeneous Dirichlet-Neumann boundary data. First, we obtain a representation formula for…
Maximally dissipative boundary conditions are applied to the initial-boundary value problem for Einstein's equations in harmonic coordinates to show that it is well-posed for homogeneous boundary data and for boundary data that is small in…
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 well-posedness is studied for the initial boundary value problem of the two-dimensional compressible ideal magnetohydrodynamic (MHD) equations in bounded perfectly conducting domains with corners. The presence of corners…
In this paper, we study a class of initial-boundary value problems for the Korteweg-de Vries equation posed on a bounded domain $(0,L)$. We show that the initial-boundary value problem is locally well-posed in the classical Sobolev space…
We derive explicit solution representations for linear, dissipative, second-order Initial-Boundary Value Problems (IBVPs) with coefficients that are spatially varying, with linear, constant-coefficient, two-point boundary conditions. We…
We employ the Ablowitz-Ladik system as an illustrative example in order to demonstrate how to analyze initial-boundary value problems for integrable nonlinear differential-difference equations via the unified transform (Fokas method). In…
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…