A transform method for linear evolution PDEs on a finite interval
From MaRDI portal
Publication:5714574
DOI10.1093/imamat/hxh047zbMath1084.35002arXivmath/0412027OpenAlexW1596130750MaRDI QIDQ5714574
Beatrice Pelloni, Athanassios S. Fokas
Publication date: 3 January 2006
Published in: IMA Journal of Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0412027
Integral representations of solutions to PDEs (35C15) Transform methods (e.g., integral transforms) applied to PDEs (35A22) Initial value problems for linear higher-order PDEs (35G10)
Related Items (47)
Well-posed two-point initial-boundary value problems with arbitrary boundary conditions ⋮ The solution of linear constant-coefficient evolution PDEs with periodic boundary conditions ⋮ Generalized Dirichlet-to-Neumann Map in Time-Dependent Domains ⋮ Exact asymmetric Skyrmion in anisotropic ferromagnet and its helimagnetic application ⋮ The time-dependent Schrödinger equation with piecewise constant potentials ⋮ A hybrid analytical–numerical method for solving evolution partial differential equations. I. The half-line ⋮ The linear KdV equation with an interface ⋮ A higher dispersion KdV equation on the half-line ⋮ Initial value problem for the time-dependent linear Schrödinger equation with a point singular potential by the unified transform method ⋮ A numerical implementation of the unified Fokas transform for evolution problems on a finite interval ⋮ Generalised Dirichlet to Neumann maps for linear dispersive equations on half-line ⋮ The initial-boundary value problem for the Sasa-Satsuma equation on a finite interval via the Fokas method ⋮ Boundary behavior for the heat equation on the half‐line ⋮ Integral representations for the double-diffusivity system on the half-line ⋮ The linear Lugiato-Lefever equation with forcing and nonzero periodic or nonperiodic boundary conditions ⋮ Boundary behavior of the solution to the linear Korteweg‐De Vries equation on the half line ⋮ A Study of Nonholonomic Deformations of Nonlocal Integrable Systems Belonging to the Nonlinear Schrödinger Family ⋮ Boundary value problems for the elliptic sine-Gordon equation in a semi-strip ⋮ The Korteweg-de Vries equation on an interval ⋮ Well-posedness of the nonlinear Schrödinger equation on the half-plane ⋮ The Fokas method for integrable evolution equations on a time-dependent interval ⋮ The Unified Transform and the Water Wave Problem ⋮ Well-posedness of a higher dispersion KdV equation on the half-line ⋮ Integrable nonlinear evolution equations on a finite interval ⋮ The generalized Dirichlet-Neumann map for linear elliptic PDEs and its numerical implementation ⋮ The Heat Equation in the Interior of an Equilateral Triangle ⋮ The nonlinear Schrödinger equation on the half-line with a Robin boundary condition ⋮ Asymptotics of linear initial boundary value problems with periodic boundary data on the half-line and finite intervals ⋮ Commutative quaternions, spectral analysis and boundary value problems ⋮ Eigenvalues for the Laplace operator in the interior of an equilateral triangle ⋮ The spectral representation of two-point boundary-value problems for third-order linear evolution partial differential equations ⋮ An example where separation of variables fails ⋮ Initial-boundary value problems for linear PDEs with variable coefficients ⋮ Boundary value problems for Boussinesq type systems ⋮ Multilayer diffusion in a composite medium with imperfect contact ⋮ A semi-analytical numerical method for solving evolution and elliptic partial differential equations ⋮ Revivals and fractalisation in the linear free space Schrödinger equation ⋮ Discrete linear evolution equations in a finite lattice ⋮ A numerical implementation of Fokas boundary integral approach: Laplace's equation on a polygonal domain ⋮ Spectral theory of some non-selfadjoint linear differential operators ⋮ Efficient numerical solution of the generalized Dirichlet-Neumann map for linear elliptic PDEs in regular polygon domains ⋮ Initial-boundary value problems for a reaction-diffusion equation ⋮ Fokas diagonalization of piecewise constant coefficient linear differential operators on finite intervals and networks ⋮ Interface Problems for Dispersive Equations ⋮ The Neumann and Robin problems for the Korteweg–de Vries equation on the half-line ⋮ Heat conduction on the ring: interface problems with periodic boundary conditions ⋮ Time-periodic linear boundary value problems on a finite interval
This page was built for publication: A transform method for linear evolution PDEs on a finite interval
