## Two-point boundary value problems for linear evolution equations

- A. Fokas, B. Pelloni
- MathematicsMathematical Proceedings of the Cambridge…
- 1 November 2001

We study boundary value problems for a linear evolution equation with spatial derivatives of arbitrary order, on the domain 0 < x < L, 0 < t < T, with L and T positive finite constants. We present a… Expand

## A transform method for linear evolution PDEs on a finite interval

- A. Fokas, B. Pelloni
- Mathematics
- 1 December 2004

We study initial boundary value problems for linear scalar evolution partial differential equations, with spatial derivatives of arbitrary order, posed on the domain {t > 0, 0 < x < L). We show that… Expand

## Unified Transform for Boundary Value Problems: Applications and Advances

- A. Fokas, B. Pelloni
- Mathematics
- 30 December 2014

This book describes state-of-the-art advances and applications of the unified transform and its relation to the boundary element method. The authors present the solution of boundary value problems… Expand

## Boundary Value Problems for Boussinesq Type Systems

- A. Fokas, B. Pelloni
- Mathematics
- 1 February 2005

Abstract
We characterise the boundary conditions that yield a linearly well posed problem for the so-called KdV–KdV system and for the classical Boussinesq system. Each of them is a system of two… Expand

## Analytical Mechanics: An Introduction

- A. Fasano, S. Marmi, B. Pelloni
- Physics, Engineering
- 2006

1. Geometric and Kinematic Foundations of Lagrangian Mechanics 2. Dynamics: General Laws and the Dynamics of a Point Particle 3. One-dimensional Motion 4. The Dynamics of Discrete Systems. Lagrangian… Expand

## The elliptic sine-Gordon equation in a half plane

- B. Pelloni, D. Pinotsis
- Mathematics
- 2009

We consider boundary value problems for the elliptic sine-Gordon equation posed in the half plane y > 0. This problem was considered in Gutshabash and Lipovskii (1994 J. Math. Sci. 68 197–201) using… Expand

## Advances in the study of boundary value problems for nonlinear integrable PDEs

- B. Pelloni
- Mathematics
- 1 February 2015

In this review I summarize some of the most significant advances of the last decade in the analysis and solution of boundary value problems for integrable partial differential equations (PDEs) in two… Expand

## The Dirichlet-to-Neumann map for the elliptic sine-Gordon equation

- A. S. Fokas, B. Pelloni
- Mathematics
- 1 April 2012

We analyse the Dirichlet problem for the elliptic sine-Gordon equation in the upper half plane. We express the solution q(x, y) in terms of a Riemann–Hilbert problem whose jump matrix is uniquely… Expand

## Spectral analysis of the elliptic sine-Gordon equation in the quarter plane

- B. Pelloni
- Mathematics
- 19 August 2009

We study the elliptic sine-Gordon equation in the quarter plane using a spectral transform approach. We determine the Riemann-Hilbert problem associated with well-posed boundary value problems in… Expand

## Non-steady-state heat conduction in composite walls

- B. Deconinck, B. Pelloni, N. Sheils
- MathematicsProceedings of the Royal Society A
- 12 February 2014

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