This paper examines a boundary value problem for a degenerate elliptic equation in a planar domain bounded by a line segment and an analytic curve. The primary objective is to construct an explicit analytical solution using the Green’s function together with singleand double-layer potential methods. A rigorous proof of the existence and uniqueness of the solution under mixed boundary conditions is presented. The degeneracy on a portion of the boundary introduces significant analytical difficulties, necessitating the use of advanced techniques in the theory of elliptic equations with singular coefficients. Furthermore, the potential applications of the model in biomedical settings, particularly in oncology, are discussed. The equation captures anomalous diffusion processes in tumor tissues, incorporating the spatial heterogeneity of the medium. This makes the model a valuable tool for analyzing the distribution of drugs, oxygen, and other substances in biological structures characterized by pronounced anisotropy and heterogeneity.
| Mualliflar | Ochilova, N.K., Очилова, Н.К. |
|---|---|
| Jurnal | Ҳисоблаш ва амалий математика муаммолари |
| Nashriyot | Тошкент ахборот технологиялари университети қошидаги, Ахборот-коммуникация технологиялари илмий-инновацион, маркази |
| ISSN | 2181-8460, 2181-046X |
| Nashr sanasi | 2026-05-02 |
| Son | 2 |
| Betlar | 16-26 |
| Til | Ingliz |
| Ilmiy soha | Fizika-matematika |
| DOI | 10.71310/pcam.2_72.2026.02 |
| Indeksga qo‘shilgan | 2026-08-27 |
DOI: 10.71310/pcam.2_72.2026.02 · Maqolaning asl sahifasi
Green’s function, potential, Jordan arc, mixed type equation, Lipschitz condition, biomedicine, oncology, tumor, anisotropy, функция Грина, потенциал, дуга Жордана, уравнение смешанного типа, условие Липшица, биомедицина, онкология, опухоль, анизотропия
| APA | Ochilova, N.K., & Очилова, Н.К. (2026). Mixed-Composite-Type Equations as a Model of Anomalous Diffusion in Tumor Tissues. Ҳисоблаш ва амалий математика муаммолари, (2), 16-26. https://doi.org/10.71310/pcam.2_72.2026.02 |
|---|---|
| GOST (OAK) | Ochilova, N.K., Очилова, Н.К. Mixed-Composite-Type Equations as a Model of Anomalous Diffusion in Tumor Tissues // Ҳисоблаш ва амалий математика муаммолари. – 2026. – № 2. – P. 16-26. – DOI: 10.71310/pcam.2_72.2026.02. |
| MLA | Ochilova, N.K., and Очилова, Н.К. “Mixed-Composite-Type Equations as a Model of Anomalous Diffusion in Tumor Tissues.” Ҳисоблаш ва амалий математика муаммолари, (2), 16-26, 2026. https://doi.org/10.71310/pcam.2_72.2026.02 |
| Chicago | Ochilova, N.K., and Очилова, Н.К. “Mixed-Composite-Type Equations as a Model of Anomalous Diffusion in Tumor Tissues.” Ҳисоблаш ва амалий математика муаммолари, (2), 16-26 (2026). https://doi.org/10.71310/pcam.2_72.2026.02 |
| Harvard | Ochilova, N.K., and Очилова, Н.К (2026) ‘Mixed-Composite-Type Equations as a Model of Anomalous Diffusion in Tumor Tissues’, Ҳисоблаш ва амалий математика муаммолари, (2), 16-26. https://doi.org/10.71310/pcam.2_72.2026.02 |
| BibTeX | @article{ochilovank2026,
title = {Mixed-Composite-Type Equations as a Model of Anomalous Diffusion in Tumor Tissues},
author = {Ochilova, N.K. and Очилова, Н.К.},
journal = {Ҳисоблаш ва амалий математика муаммолари},
year = {2026},
number = {2},
pages = {16-26},
doi = {10.71310/pcam.2_72.2026.02},
url = {https://doi.org/10.71310/pcam.2_72.2026.02}
} |
Boshqa maqola uchun iqtibos tayyorlash
The problem of constructing optimal quadrature formulas for approximate calculation of definite integrals and approximation of functions is one of the important problems of computational mathematics. These problems have…
The method of displaced nodes is applied when solving the Dirichlet problem for the Poisson equation in a rectangular domain. By approximating the Laplace operator using moving nodes, we obtain an approximate analytical…
The solutions of boundary value problems associated with two-parameter singularly perturbed differential equations are well known to exhibit the formation of two distinct boundary layers, typically occurring near the…
The discovery of new chemical compounds with specified properties is a challenging problem in drug development. Many studies encode molecules as string representations derived from molecular graphs; however, this…
This paper examines the dynamic modes of the fractional Zeeman oscillator. The fractional Zeeman oscillator is a system of two ordinary differential equations with fractional derivatives, understood in the…
This research develops a mathematical formulation and numerical solution for the spatial-temporal distribution of groundwater head in heterogeneous porous media. Based on Darcy’s and mass conservation laws, a 3D…
Recent years have witnessed significant climatic changes and increasing environmental pressure globally, including in Uzbekistan, necessitating an objective regional assessment. This research develops an approach for…
This research presents a multidimensional mathematical model and a robust secondorder numerical algorithm for coupled heat and moisture transfer with pressure-driven gas flow. Utilizing fractional Caputo derivatives (0…
This article presents a mathematical model and algorithm for numerically solving a problem for studying the hydrodynamic process of in-situ leaching in a heterogeneous porous medium, taking into account mass transfer…
This article presents a highly accurate and efficient method—a discrete version of the preintegration method—for numerically solving the Cauchy problem for a singularly perturbed third-order equation. The method is…
Ҳисоблаш ва амалий математика муаммолари — barcha maqolalar · 2026-yil arxivi
We study a family of degenerate-singular second- and third-order elliptic boundary value problems modeling anomalous diffusion in heterogeneous tumor tissue, all built on one differential operator with a power-law…
This article presents the results of 2018-2023, such as biological diversity, inter-landscape distribution characteristics, density,and number of straggly insects identified from natural and anthropogenic areas of…
This article observational data on the species composition, distribution, population, density, and seasonal damage caused causedby herbivorus bugs. Observationes were carried out in April and September 2021. When…
In the article, the research fields of some species belonging to Paeonia, their significance in human life, adaptation features tovarious ecological conditions are highlighted, and the ecologist groups and other…
This article studies the number of species, population density of terrestrial mollusks of the Topalangdarya basin, located in theSurkhandarya region of Uzbekistan, in various altitudinal regions and biotopes and…
This article sheds light on changes in biomass formation and antimicrobial activity against test pathogenic strains under theinfluence of epigenetic modifiers and elicitors of the endophytic fungus Penicillium…
Shahimardonsoy covered issues such as the soil in the river basin and measures to increase its condition, salinity and fertility, theflora and fauna present in the basin landscape and their conservation.