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

@article{Smith2019LinearEE, title={Linear evolution equations on the half-line with dynamic boundary conditions}, author={D. A. Smith and Wei Yan Toh}, journal={arXiv: Analysis of PDEs}, year={2019} }

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 $bq(0,t)+q_x(0,t)=0$ is replaced with a dynamic Robin condition; $b=b(t)$ is allowed to vary in time. We present a solution representation, and justify its validity, via an extension of the Fokas transform method. We show how to reduce the problem to a variable coefficient fractional linear ordinary differential…

## 4 Citations

### 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…

### 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…

### Fokas diagonalization

- Mathematics
- 2022

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 unified transform for evolution equations on the half‐line with time‐periodic boundary conditions *

- MathematicsStudies in Applied Mathematics
- 2021

This paper elaborates on a new approach for solving the generalized Dirichlet‐to‐Neumann map, in the large time limit, for linear evolution PDEs formulated on the half‐line with time‐periodic…

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