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…