The annotation of the dissertation of Master Degree

MINISTRY OF HIGHER AND SECONDARY EDUCATION OF THE REPUBLIC OF UZBEKISTAN
SAMARKAND STATE UNIVERSITY

Faculty: Digital technologies Department: Mathematical modeling Academic year : 2019-2021

Master student: Ruziyeva M Supervisor : Khuzhayorov B Specialty: 5A130202- Applied mathematics and information technologies

THE ANNOTATION OF THE MASTER’S THESIS
Actuality of subject: It is important to determine the parameters of the mathematical model of the anomalous strength of matter in porous media. There are various ways to determine the parameters of the model, including by experiment, which can be determined by solving inverse problems. Due to the complexity of the experiment, one of the most effective ways to determine the values of the model parameters by solving inverse problems with coefficients.
Study objectives: The aim of this work is to numerically solve the coefficients of inverse problems for an equation of the parabolic type. Goal management, job management tasks are set:
- to study inverse problems for parabolic equations, their classification, theory and methods of solution;
- Solve the inverse problem with coefficient for the diffusion equation;
- Solve the inverse problem with the coefficient of anomalous strength of the substance in a porous medium.
Object and subject of study: The process of migration of matter in a porous environment
The degree of novelty of study results: The dissertation solves the inverse problem of the coefficient of displacement of matter in a porous medium. On the basis of solving the inverse problem, the diffusion coefficient in the displacement equations and the cost of the source coefficient are determined. The stability of the solution was made to the errors of the initial data.
Structure of thesis: This dissertation consists of an introduction, three chapters, conclusion, literature, application and scientific theses..
Main results of thesis: The right questions were put to work and they were solved numerically. Using the solution of the correct problems, the inverse problems of the coefficient of strength of the anomalous substance are solved. The problems were solved in one- and two-dimensional form, and the variable of the coefficient sought was found in the equation.

Supervisor B. Khuzhayorov
Master student M.Ruziyeva