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On the Kneser property for reaction-diffusion equations in some unbounded domains with an H^{-1}-valued non-autonomous forcing term
(Elsevier, 2012)
In this paper we prove the Kneser property for a reaction-diffusion equation on an unbounded domain satisfying the Poincaré inequality with an external force taking values in the space H^{−1}. Using this property of solutions ...
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Homogenization of an incompressible non-Newtonian flow through a thin porous medium
(Springer, 2017)
In this paper, we consider a non-Newtonian flow in a thin porous medium Ωε of thickness ε which is perforated by periodically solid cylinders of size aε. The flow is described by the 3D incompressible Stokes system with a ...
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Derivation of a coupled Darcy-Reynolds equation for a fluid flow in a thin porous medium including a fissure
(Springer, 2017)
We study the asymptotic behavior of a fluid flow in a thin porous medium of thickness ε, which characteristic size of the pores ε, and containing a fissure of width ηε. We consider the limit when the size of the pores ...
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Attractors for a non-autonomous Liénard equation
(World Scientific Publishing, 2015)
In this paper we prove the existence of pullback and uniform attractors for a non-autonomous Liénard equation. The relation among these attractors is also discussed. After that, we consider that the Liénard equation includes ...
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Asymptotic behaviour of nonlocal reaction-diffusion equations
(Elsevier, 2010)
The existence of a global attractor in L^2(Ω) is established for a reaction-diffusion equation on a bounded domain Ω in R^d with Dirichlet boundary conditions, where the reaction term contains an operator F : L^2(Ω) → ...
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Analysis of the effects of a fissure for a non-Newtonian fluid flow in a porous medium
(International Press, 2018)
We study the solution of a non-Newtonian flow in a porous medium which characteristic size of the pores ε and containing a fissure of width ηε. The flow is described by the incompressible Stokes system with a nonlinear ...
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Sharp Pressure Estimates for the Navier–Stokes System in Thin Porous Media
(Springer, 2023-04-16)
A relevant problem for applications is to model the behavior of Newtonian fluids through thin porous media, which is a domain with small thickness and perforated by periodically distributed cylinders of size and period ...
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Asymptotic behaviour of the nonautonomous SIR equations with diffusion
(American Institute of Mathematical Sciences (AIMS), 2014)
The existence and uniqueness of positive solutions of a nonautonomous system of SIR equations with diffusion are established as well as the continuous dependence of such solutions on initial data. The proofs are facilitated ...
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On the non-stationary non-Newtonian flow through a thin porous medium
(Wiley, 2017)
We consider a non-stationary incompressible non-Newtonian flow in a thin porous medium of thickness ε which is perforated by periodically distributed solid cylinders of size aε. The viscosity is supposed to obey the power ...
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Homogenization of a non-stationary non-Newtonian flow in a porous medium containing a thin fissure
(Cambridge University Press, 2018-02-05)
We consider a non-stationary incompressible non-Newtonian Stokes system in a porous medium with characteristic size of the pores ε and containing a thin fissure of width ηε. The viscosity is supposed to obey the power law ...