The aim of this paper is to study the global existence in time of solutions for some class of reaction-diffusion systems. Our techniques of proof is based on compact semigroup methods and some L 1 estimates. Our goal is to show, under suitable assumptions, that the proposed model have a global solution for a large class of the functions f and g.
The purpose of this paper is to prove the global existence of solution for one of most significant fractional partial differential system called the fractional reaction-diffusion system. This will be carried out by combining the compact semigroup methods with some L1-estimate methods. Our investigation can be applied to a wide class of fractional partial differential equations even if they contain nonlinear terms in their constructions.
In this paper, we study global existence of weak solutions for 2 × 2 parabolic reaction-diffusion systems with a full matrix of diffusion coefficients on a bounded domain, such as, we treat the main properties related: the positivity of the solutions and the total mass of the components are preserved with time. Moreover, we suppose that the non-linearities have critical growth with respect to the gradient. The technique used is based on compact semigroup methods and some estimates. Our objective is to show, under appropriate hypotheses, that the proposed model has a global solution with a large choice of non-linearities.
The aim of this paper is to prove that asymptotic behavior in the time of solutions for the weakly coupled reaction diffusion system:∂ui/∂t − di∆ui = fi (u1, u2, …, um) in Ω×R+,∂ui/∂η = 0 in ∂Ω×R+, (0.1)ui(., 0) = ui0(.) in Ω,where Ω is an open bounded domain of class C1 in Rn, ui(t, x), i=1, m, t≥0, x∈Ω are real valued functions. We treat the system (0.1) as a dynamical system in C(Ω) × C(Ω) × ... × C(Ω) and apply Lyapunov type stability techniques. A key ingredient in this analysis is a result which establishes that the orbits of the dynamical system are precompact in C(Ω) × C(Ω) × ... × C(Ω). As a consequence of Arzela-Ascoli theorem, this will be satisfied if the orbits are, for example, uniformly bounded in C1(Ω) × C1(Ω) × ... × C1(Ω) for t>0.
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