TY - JOUR
AU - Zharullayev, D. B.
AU - Kanguzhin, B. E.
AU - Konyrkulzhayeva, M. N.
PY - 2019/04/23
Y2 - 2024/10/05
TI - Green's function of differential operators on a star-shaped graph with common boundary conditions
JF - Journal of Mathematics, Mechanics and Computer Science
JA - JMMCS
VL - 101
IS - 1
SE - Mathematics
DO - 10.26577/JMMCS-2019-1-601
UR - https://bm.kaznu.kz/index.php/kaznu/article/view/601
SP - 48-58
AB - <p>Differential equations on graphs are one of the new sections of the theory of differential equations<br>and their fundamental concepts when analyzing models of a wide variety of problems in natural<br>science. It also arises when analyzing processes in complex systems, allowing as a set of onedimensional<br>continuum that interact only through the ends. The differential operator on graphs<br>is currently actively studying by mathematics and is found in many different applications, for<br>example, chemical kinetics, chemical technology, quantum mechanics, nanotechnology, biology,<br>organic chemistry, Markov processes, etc. In this paper, we construct the Green function of a<br>differential operator on a star shaped graph with common boundary conditions. In this paper, a<br>star shaped graph is a tree with one internal vertex and m leaves. Standard Kirchhoff conditions<br>are used at the interior vertices and mixed conditions at the boundary vertices. The edges of the<br>graph is a one-dimensional smooth regular manifold (curve). The top of the graph is a point.<br>The applicability of the results of this study is high both in theoretical terms - the development of<br>research in the theory of differential equations with memory on graphs, and in terms of applications<br>to biological processes, in particular neurobiology, nanotechnology, in the chemical and petroleum<br>industries.</p>
ER -