Recently, the cross-diffusion problem has gained importance in solving problems of mathematical modelling of complex processes such as population dynamics, diffusion in multiphase media and reaction-diffusion systems and therefore has attracted considerable attention. Studies have shown that cross-diffusion elements in models can significantly change the qualitative and quantitative properties of solutions. However, many aspects of solutions, especially nonlinear boundary value problems, have not been sufficiently studied, which requires further and more in-depth study of these issues and creates the need for a more in-depth theoretical analysis. Based on the above considerations, the objective of this study is to formulate and analyse the scientific problem associated with the dynamic behaviour of the cross-diffusion problem based on the conditions of existence and non-existence of a global solution and the influence of boundary and parametric conditions on solutions based on self-similar analysis. The research methodology is based on the use of a self-similar approach, which allows simplifying the system of differential equations by introducing variables that are invariant with respect to changes in measurements. The main conclusion of the work is that the use of self-similar variables not only significantly simplifies the study of complex cross-diffusion models but also allows us to obtain important information about the stability limits of solutions.
| Mualliflar | Rakhmonov, Zafar, Urunbaev, Jasur, Joniev, Akmal |
|---|---|
| Jurnal | Innovative Multidisciplinary Journal of Applied Technology |
| Nashr sanasi | 2025-10-28 |
| Jild | 3 |
| Son | 10 |
| Betlar | 128-132 |
| Til | Ingliz |
| DOI | 10.51699/pc7z5g80 |
DOI: 10.51699/pc7z5g80 · Maqolaning asl sahifasi
self-similar analysis nonlinear parabolic system, cross-diffusion, diffusion, critical exponents of the Fujita type, blow-up, existence, non-existence
Wireless capsule endoscopy (WCE) produces long, variable-quality video streams in which early and reliable polyp detection is critical. We present YOLO-InceptionResNet-A, a lightweight object detector that replaces the…
The subject of steganography is the means and methods that ensure the concealment of the fact of message transmission. The historical roots of this discipline are very deep. With the development of technology, the…
In this work, a technological process for the production of the "Cover" part by hot stamping under medium-volume production conditions is designed. The purpose of the work is to improve the technological level of…
This article creates and assesses a supervX`ised machine learning model in order to forecast spot truckload rates at the shipment level, this paper. We create a feature set with lane information, shipment date…
The inclusion of recycled jute fibers in soil is gaining attention as a sustainable method for enhancing soil strength characteristics. This overview article examines the impact of integrating jute fibers into soil on…
The advancement of patient bed technology has been driven by the integration of embedded systems and the Internet of Things (IoT), enhancing functionality and patient care. Despite the increasing demand for smart…
Rigid pavements, commonly composed of Portland Cement Concrete (PCC), are crucial infrastructure elements due to their durability and load-bearing capacity. This review paper synthesizes research on the performance…
The smart medical cart represents a paradigm shift in healthcare logistics, leveraging cutting-edge technology to enhance the distribution of medical supplies. The integration of an Arduino Uno microcontroller and…
Cloud computing has revolutionized modern IT infrastructure by offering scalable and on-demand resource provisioning. However, the dynamic nature of cloud workloads presents significant challenges in efficient resource…
The research examines how beneficial local climate factors impact lifespan for humans while affecting building preservation periods. The growing worldwide focus on sustainable energy usage and productivity requires…
Innovative Multidisciplinary Journal of Applied Technology — barcha maqolalar