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Local Bifurcations in a Nonlinear Model of a Bioreactor

Dimitrova, Neli (2009)

Serdica Journal of Computing

This paper is partially supported by the Bulgarian Science Fund under grant Nr. DO 02– 359/2008.We consider a nonlinear model of a continuously stirred bioreactor and study the stability of the equilibrium points with respect to practically important model parameters. We determine regions in the parameter space where the steady states undergo transcritical and Hopf bifurcations. In the latter case, the stability of the emerged limit cycles is also studied. Numerical simulations in the computer algebra...

Local center manifold for parabolic equations with infinite delay

Hana Petzeltová (1994)

Mathematica Bohemica

The existence and attractivity of a local center manifold for fully nonlinear parabolic equation with infinite delay is proved with help of a solutions semigroup constructed on the space of initial conditions. The result is applied to the stability problem for a parabolic integrodifferential equation.

Local Controllability around Closed Orbits

Marek Grochowski (2014)

Bulletin of the Polish Academy of Sciences. Mathematics

We give a necessary and sufficient condition for local controllability around closed orbits for general smooth control systems. We also prove that any such system on a compact manifold has a closed orbit.

Local exact controllability to the trajectories of the Navier-Stokes system with nonlinear Navier-slip boundary conditions

Sergio Guerrero (2006)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we deal with the local exact controllability of the Navier-Stokes system with nonlinear Navier-slip boundary conditions and distributed controls supported in small sets. In a first step, we prove a Carleman inequality for the linearized Navier-Stokes system, which leads to null controllability of this system at any time T>0. Then, fixed point arguments lead to the deduction of a local result concerning the exact controllability to the trajectories of the Navier-Stokes system.

Local Lipschitz continuity of the stop operator

Wolfgang Desch (1998)

Applications of Mathematics

On a closed convex set Z in ℝ N with sufficiently smooth ( 𝒲 2 , ∞ ) boundary, the stop operator is locally Lipschitz continuous from 𝐖 1 , 1 ( [ 0 , T ] , ℝ N ) × Z into 𝐖 1 , 1 ( [ 0 , T ] , ℝ N ) . The smoothness of the boundary is essential: A counterexample shows that 𝒞 1 -smoothness is not sufficient.

Local properties of the solution set of the operator equation in Banach spaces in a neighbourhood of a bifurcation point

Joanna Janczewska (2004)

Open Mathematics

In this work we study the problem of the existence of bifurcation in the solution set of the equation F(x, λ)=0, where F: X×R k →Y is a C 2-smooth operator, X and Y are Banach spaces such that X⊂Y. Moreover, there is given a scalar product 〈·,·〉: Y×Y→R 1 that is continuous with respect to the norms in X and Y. We show that under some conditions there is bifurcation at a point (0, λ0)∈X×R k and we describe the solution set of the studied equation in a small neighbourhood of this point.

Localization of nonsmooth lower and upper functions for periodic boundary value problems

Irena Rachůnková, Milan Tvrdý (2002)

Mathematica Bohemica

In this paper we present conditions ensuring the existence and localization of lower and upper functions of the periodic boundary value problem u ' ' + k u = f ( t , u ) , u ( 0 ) = u ( 2 π ) , u ' ( 0 ) = u ' ( 2 π ) , k ∈ ℝ , k ≠ 0 . These functions are constructed as solutions of some related generalized linear problems and can be nonsmooth in general.

Logistic equations in tumour growth modelling

Urszula Foryś, Anna Marciniak-Czochra (2003)

International Journal of Applied Mathematics and Computer Science

The aim of this paper is to present some approaches to tumour growth modelling using the logistic equation. As the first approach the well-known ordinary differential equation is used to model the EAT in mice. For the same kind of tumour, a logistic equation with time delay is also used. As the second approach, a logistic equation with diffusion is proposed. In this case a delay argument in the reaction term is also considered. Some mathematical properties of the presented models are studied in...

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