Differential Equations on Networks (Geometric Graphs)

Pokornyi, Yu. V.; Borovskikh, A. V.

doi:10.1023/b:joth.0000012752.77290.fa

Cited by 132 publications

(112 citation statements)

References 33 publications

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“…For more details about c 2014 Diogenes Co., Sofia pp. 499-510 , DOI: 10.2478/s13540-014-0182-4 differential equations and BVPs on graphs, as well as their applications, the reader is referred to [3,5,6,9,10,21,22,23] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Existence and uniqueness of solutions for a fractional boundary value problem on a graph

Graef

Kong

Wang

2014

fcaa

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Section: Introductionmentioning

confidence: 99%

Existence and uniqueness of solutions for a fractional boundary value problem on a graph

Graef

Kong

Wang

2014

fcaa

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“…Differential operators on graphs networks, trees often appear in mathematics, mechanics, physics, geophysics, physical chemistry, electronics, nanoscale technology and branches of natural sciences and engineering see 1-7 and the bibliographies thereof . In recent years there has been considerable interest in the spectral theory of Sturm-Liouville operators on graphs see [8][9][10] . The direct spectral and scattering problems on compact and noncompact graphs, respectively, were considered in many publications see, e.g., [11][12][13][14][15] .…”

Section: Introductionmentioning

confidence: 99%

An Inverse Spectral Problem for the Sturm-Liouville Operator on a Three-Star Graph

Tazehkand

Akbarfam

2012

ISRN Applied Mathematics

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We study an inverse spectral problem for the Sturm-Liouville operator on a three-star graph with the Dirichlet and Robin boundary conditions in the boundary vertices and matching conditions in the internal vertex. As spectral characteristics, we consider the spectrum of the main problem together with the spectra of two Dirichlet-Dirichlet problems and one Robin-Dirichlet problem on the edges of the graph and investigate their properties and asymptotic behavior. We prove that if these four spectra do not intersect, then the inverse problem of recovering the operator is uniquely solvable. We give an algorithm for the solution of the inverse problem with respect to this quadruple of spectra.

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“…Here a connected graph is defined as an union of 0-D vertices that links 1-D intervals [6]. These PDEs have served as important mathematical tools to analyze, predict, and control the transport phenomena.…”

Section: Introductionmentioning

confidence: 99%

Numerical modelling of nonlinear and degenerate diffusion equations on connected graphs: application to moisture dynamics in non-woven fibrous strip networks

2016

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A numerical model of a nonlinear and degenerate diffusion equation on connected graphs, arising in a diversity of industrial applications, is presented. This paper shows that concurrently using a staggered finite volume spatial discretization with an analytical solution-based flux evaluation method and an operator-splitting technique computes stable and physicallyconsistent numerical solutions to the equation. A demonstrative application example of the numerical model to moisture dynamics in a hypothetical non-woven fibrous strip network under an evaporative environment is presented in order to show its versatility. Mathematical issues to be addressed in a future for better comprehending the model are finally discussed.

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Differential Equations on Networks (Geometric Graphs)

Cited by 132 publications

References 33 publications

Existence and uniqueness of solutions for a fractional boundary value problem on a graph

Existence and uniqueness of solutions for a fractional boundary value problem on a graph

An Inverse Spectral Problem for the Sturm-Liouville Operator on a Three-Star Graph

Numerical modelling of nonlinear and degenerate diffusion equations on connected graphs: application to moisture dynamics in non-woven fibrous strip networks

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