Abstract
In this paper, we are interested in the study of a degenerate reaction-diffusion model, where we prove the existence of positive maximal and minimal solutions, including the uniqueness of the positive solution. The technique used is mainly based on the method of upper and lower solutions.
Highlights
We shall study the following system recent years, in the study of reaction-diffusion systems, due to their paramount importance and frequent use in the modeling of many diffusion phenomena that we observe in (1.1):
In Ω on ∂Ω, where Ω is a bounded domain in Rn (n ≥ 2) with nature and which result from various natural sciences and engineering, such as (Coronavirus, hepatitis, population dynamics, migration of biological species, quenching)
In Murray [13,14], we find many real models in different boundary ∂Ω
Summary
[15,16,17,18]. We shall study the following system recent years, in the study of reaction-diffusion systems, due to their paramount importance and frequent use in the modeling of many diffusion phenomena that we observe in (1.1):. In a homogeneous porous medium with an isentropic flow He can model the steady state of phenomena such as the type of problems. The rest of this paper is organized as follows: In the and in many problems of physics, engineering, biology, section, we state our main result. Degenerate systems, we mention for example Alaa et al [2], we give some results regarding the approximate problem. To achieve the desired result, we will use a technique based mainly on the method of upper and lower solutions. ÛN) in C2(Ω) ∩ C(Ω ) are called ordered upper and lower solutions of (1.1) if ûs ≤ ũs and (2.1): {−ûdi(ixv)(D≤(uĝii)(∇x)û i,) 1≤≤f(ix≤, ûNs) in Ω on ∂Ω, and ũi satisfies (2.1) with inequalities reversed. 0, and that is exactly what we want to get
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