In: Journal of Mathematical Analysis and Applications, 2010, p. -
In this paper we consider the two species competitive delay plankton allelopathy stimulatory model system. We show the existence and uniqueness of the solution of the deterministic model. Moreover, we study the persistence of the model and the stability properties of its equilibrium points. We illustrate the theoretical results by some numerical simulations.
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In: Variational Problems in Riemannian Geometry, 2004, p. 45-64
Let M and N be compact smooth Riemannian manifolds without boundaries. Then, for a map u : M→N, we consider a class of energies which includes the popular Dirichlet energy and the more general p-energy. Geometric or physical questions motivate to investigate the critical points of such an energy or the corresponding heat flow problem. In the case of the Dirichlet energy, the heat flow...
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In: International Journal of Pure and Applied Mathematics, 2004, vol. 14, no. 2, p. 241-267
We study a Navier-Stokes system which is motivated by models for electrorheological fluids. Its principal features are the weak monotonicity assumptions we impose on the viscosity tensor. Moreover we allow the viscosity to depend on the velocity in order to cover some of the models in electrorheological theory. We establish existence of a weak solution of the corresponding Navier-Stokes...
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In: International Journal of Differential Equations and Applications
We (Dreyfuss P., Hungerbühler, N., 2004, Int. J. of Pure and Appl.Math. 14(2): 241– 271) investigated a class of Navier-Stokes systems which is motivated by models for electrorheological fluids. We obtained an existence result for a weak solution under mild monotonicity assumptions for the viscosity tensor. In this article, we continue the analysis of such systems, but with various notions...
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In: Electronic Journal of Differential Equations, 2004, vol. 144, p. 1-18
We study the quasilinear elliptic system −div σ(x, u,Du) = v(x) + f(x, u) + div g(x, u) on a bounded domain of Rⁿ with homogeneous Dirichlet boundary conditions. This system corresponds to a diffusion problem with a source v in a moving and dissolving substance, where the motion is described by g and the dissolution by f. We prove existence of a weak solution of this system under classical...
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