# The unified transform method for linear initial-boundary value problems: a spectral interpretation

@article{Smith2014TheUT, title={The unified transform method for linear initial-boundary value problems: a spectral interpretation}, author={David A. Smith}, journal={arXiv: Spectral Theory}, year={2014} }

AbstractIt is known that the uni ed transform method may be used to solve any well-posed initial-boundary value problem for a linear constant-coecient evolution equation on the nite in-terval or the half-line. In contrast, classical methods such as Fourier series and transformtechniques may only be used to solve certain problems. The solution representation obtainedby such a classical method is known to be an expansion in the eigenfunctions or generalisedeigenfunctions of the self-adjoint…

## 7 Citations

### Evolution PDEs and augmented eigenfunctions. Half-line

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- 2014

The solution of an initial-boundary value problem for a linear evolution partial differential equation posed on the half-line can be represented in terms of an integral in the complex (spectral)…

### Linear evolution equations on the half-line with dynamic boundary conditions

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The classical half line Robin problem for the heat equation may be solved via a spatial Fourier transform method. In this work, we study the problem in which the static Robin condition…

### Fokas diagonalization

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A method for solving linear initial boundary value problems was recently reimplemented as a true spectral transform method. As part of this reformulation, the precise sense in which the spectral…

### The diffusion equation with nonlocal data

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### Fokas Diagonalization of Piecewise Constant Coefficient Linear Differential Operators on Finite Intervals and Networks

- MathematicsActa Applicandae Mathematicae
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We describe a new form of diagonalization for linear two point constant coefficient differential operators with arbitrary linear boundary conditions. Although the diagonalization is in a weaker sense…

### LIST OF OPEN PROBLEMS AIM WORKSHOP: MATHEMATICAL ASPECTS OF PHYSICS WITH NON-SELF-ADJOINT OPERATORS *Open problems suggested during the meeting

- Mathematics
- 2015

2.1. Schauder bases of periodic functions and multipliers. Let en(x) := √ 2 sin(nπx). Then {en} is a Schauder basis of L(0, 1) for all p > 1. Let f ∈ C(R,C) satisfy f(x + 2) = f(x), f(−x) = −f(x),…

### Fokas Diagonalization of Piecewise Constant Coefficient Linear Differential Operators on Finite Intervals and Networks

- MathematicsActa Applicandae Mathematicae
- 2022

We describe a new form of diagonalization for linear two point constant coefficient differential operators with arbitrary linear boundary conditions. Although the diagonalization is in a weaker sense…

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