The diffusion equation with nonlocal data

@article{Miller2017TheDE,
  title={The diffusion equation with nonlocal data},
  author={Peter D. Miller and David A. Smith},
  journal={Journal of Mathematical Analysis and Applications},
  year={2017}
}

Figures from this paper

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

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

Fokas diagonalization

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

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

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

Kernel density estimation with linked boundary conditions

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

References

SHOWING 1-10 OF 28 REFERENCES

Nonlocal and Multipoint Boundary Value Problems for Linear Evolution Equations

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

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

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

  • B. Pelloni
  • Mathematics
    Mathematical 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

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

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

  • B. Pelloni
  • Mathematics
    Proceedings 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

  • David A. Smith
  • Mathematics
    Mathematical 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

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

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