Article

PROPERTIES OF SOLUTIONS FOR A NONLINEAR DIFFUSION PROBLEM WITH A GRADIENT NONLINEARITY

Zafar RakhmonovNational University of Uzbekistan 100174 Tashkent, UZBEKISTANA.A. AlimovTashkent Branch of the G.V. Plekhanov Russian University of Economics, UZBEKISTAN

International Journal of Apllied Mathematicsjournal2023en

ABI

Abstract

This paper studies the properties of solutions for a nonlinear diffusion problem with a gradient nonlinearity.The problem is formulated as a partial differential equation with a nonlinear term that depends on both the solution and its gradient.The main results are: existence and uniqueness of weak solutions in suitable function spaces; regularity and positivity of solutions; asymptotic behavior of solutions as time goes to infinity; comparison principles and maximum principles for solutions.The proofs are based on variational methods, fixed point arguments, energy estimates, and comparison techniques.Some examples and applications are also given to illustrate the features of the problem.

Topics

Differential Equations and Numerical Methods Differential Equations and Boundary Problems Nonlinear Differential Equations Analysis

Identifiers

DOI: 10.12732/ijam.v36i3.7

Citations and references

Cited by 1 20 references

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