INTEGRAL EQUATIONS AND THE SOLUTION OF BOUNDARY VALUE PROBLEMS FOR DIFFUSIONS AND DISPERSIVE EQUATIONS

We study the solution of boundary value problems (BVPs) via integral equation techniques. We are interested in BVPs arising in the theory of diffusions, as well as third-order dispersive equations. Our tools are classical but we also solve some new integral equations. We will produce solutions for certain Robin problems by reducing an integral equation to the inversion of a Fourier sine transform. Then we exploit a result of Titchmarsh from 1924 to produce solutions to BVPs of Dirichlet type for an important class of PDEs.

Authors

Publication Details

Journal
Journal of Integral Equations and Applications
Published
2025-03-01
DOI
https://doi.org/10.1216/jie.2025.37.7
Primary Topic
Differential Equations and Numerical Methods
Type
article
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article

INTEGRAL EQUATIONS AND THE SOLUTION OF BOUNDARY VALUE PROBLEMS FOR DIFFUSIONS AND DISPERSIVE EQUATIONS

Mark Craddock
Journal of Integral Equations and Applications
Differential Equations and Numerical Methods
article

INTEGRAL EQUATIONS AND THE SOLUTION OF BOUNDARY VALUE PROBLEMS FOR DIFFUSIONS AND DISPERSIVE EQUATIONS

Mark Craddock
article en

Abstract

We study the solution of boundary value problems (BVPs) via integral equation techniques. We are interested in BVPs arising in the theory of diffusions, as well as third-order dispersive equations. Our tools are classical but we also solve some new integral equations. We will produce solutions for certain Robin problems by reducing an integral equation to the inversion of a Fourier sine transform. Then we exploit a result of Titchmarsh from 1924 to produce solutions to BVPs of Dirichlet type for an important class of PDEs.

Journal of Integral Equations and ApplicationsVol. 37(1)
Reduced inequalities
Openalex Percentile: Top 81%
Differential Equations and Numerical Methods
DOISourceOpenAlex
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INTEGRAL EQUATIONS AND THE SOLUTION OF BOUNDARY VALUE PROBLEMS FOR DIFFUSIONS AND DISPERSIVE EQUATIONS — Mark Craddock · Journal of Integral Equations and Applications (2025) | TGRS Research Map | TGRS