## 9 Citations

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

- Mathematics
- 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…

### A hybrid analytical-numerical method for solving advection-dispersion problems on a half-line

- Computer Science, MathematicsInternational Journal of Heat and Mass Transfer
- 2019

### 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…

### 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…

### Solving PDEs of fractional order using the unified transform method

- MathematicsAppl. Math. Comput.
- 2018

### Kernel density estimation with linked boundary conditions

- MathematicsStudies in Applied Mathematics
- 2020

Kernel density estimation on a finite interval poses an outstanding challenge because of the well‐recognized bias at the boundaries of the interval. Motivated by an application in cancer research, we…

### Boundary behavior of the solution to the linear Korteweg‐De Vries equation on the half line

- MathematicsStudies in Applied Mathematics
- 2022

## References

SHOWING 1-10 OF 28 REFERENCES

### Nonlocal and Multipoint Boundary Value Problems for Linear Evolution Equations

- Mathematics
- 2015

We derive the solution representation for a large class of nonlocal boundary value problems for linear evolution partial differential equations (PDE) with constant coefficients in one space variable.…

### The Linear KdV Equation with an Interface

- Mathematics
- 2015

The interface problem for the linear Korteweg–de Vries (KdV) equation in one-dimensional piecewise homogeneous domains is examined by constructing an explicit solution in each domain. The location of…

### A Unified Approach To Boundary Value Problems

- Mathematics
- 2008

This book presents a new approach to analyzing initial-boundary value problems for integrable partial differential equations (PDEs) in two dimensions, a method that the author first introduced in…

### Well-posed boundary value problems for linear evolution equations on a finite interval

- MathematicsMathematical Proceedings of the Cambridge Philosophical Society
- 2004

We identify the class of smooth boundary conditions that yield an initial-boundary value problem admitting a unique smooth solution for the case of a dispersive linear evolution PDE of arbitrary…

### Interface Problems for Dispersive Equations

- Mathematics
- 2015

The interface problem for the linear Schrödinger equations in one‐dimensional piecewise homogeneous domains is examined by providing an explicit solution in each domain. The location of the…

### The Unified Transform for a Class of Reaction-Diffusion Problems with Discontinuous Time Dependent Parameters

- Mathematics
- 2015

Reaction-diffusion mathematical models for studying, among others, highly diffusive brain tumors, that also take into account the heterogeneity of the brain tissue, are frequently used in recent…

### The spectral representation of two-point boundary-value problems for third-order linear evolution partial differential equations

- MathematicsProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- 2005

We use a spectral transform method to study general boundary-value problems for third-order, linear, evolution partial differential equations with constant coefficients, posed on a finite space…

### Well-posed two-point initial-boundary value problems with arbitrary boundary conditions

- MathematicsMathematical Proceedings of the Cambridge Philosophical Society
- 2011

Abstract We study initial-boundary value problems for linear evolution equations of arbitrary spatial order, subject to arbitrary linear boundary conditions and posed on a rectangular 1-space, 1-time…

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

- Mathematics
- 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)…

### A Galerkin procedure for the diffusion equation subject to the specification of mass

- Mathematics
- 1987

Continuous and discrete Galerkin procedures are derived and analyzed for the numerical solution of the diffusion equation $U_1 = U_{xx} ,0 < x < 1,0 < t \leqq T,U(x,0) = f(x),U_x (1,t) = g(t)$ and…