Dynamic stabilization of systems via decoupling techniques
Dynamic stabilization of systems via decoupling techniques
We give sufficient conditions which allow the study of the exponential stability of systems closely related to the linear thermoelasticity systems by a decoupling technique. Our approach is based on the multipliers technique and our result generalizes (from the exponential stability point of view) the earlier one obtained by Henry et al.
Dynamical instability of symmetric vortices.
Using the Maxwell-Higgs model, we prove that linearly unstable symmetric vortices in the Ginzburg-Landau theory are dynamically unstable in the H1 norm (which is the natural norm for the problem).In this work we study the dynamic instability of the radial solutions of the Ginzburg-Landau equations in R2 (...)
Dynamics and patterns of an activator-inhibitor model with cubic polynomial source
The dynamics of an activator-inhibitor model with general cubic polynomial source is investigated. Without diffusion, we consider the existence, stability and bifurcations of equilibria by both eigenvalue analysis and numerical methods. For the reaction-diffusion system, a Lyapunov functional is proposed to declare the global stability of constant steady states, moreover, the condition related to the activator source leading to Turing instability is obtained in the paper. In addition, taking the...
Dynamics of Erythroid Progenitors and Erythroleukemia
The paper is devoted to mathematical modelling of erythropoiesis, production of red blood cells in the bone marrow. We discuss intra-cellular regulatory networks which determine self-renewal and differentiation of erythroid progenitors. In the case of excessive self-renewal, immature cells can fill the bone marrow resulting in the development of leukemia. We introduce a parameter characterizing the strength of mutation. Depending on its value, leukemia will or will not develop. The simplest...
Eigenvalues of inequalities of reaction-diffusion type and destabilizing effect of unilateral conditions
Einschliessungsaussagen bei Systemen semilinearer parabolischer Differentialgleichungen
Für die Lösungen seminlinearer parabolischer Differentialgleichungen werden Einschliessungsaussagen hergeleitet. Hierbei werden Aussagen zur Stabilität von Lösungen ermittelt. Die Resultate werden am Beispiel der Fitzhugh-Nagumo Gleichungen diskutiert.
Entire positive solution to the system of nonlinear elliptic equations.
Equilibrium points for a wave equation with boundary control containing an integral term. (Points d'équilibre pour une équation des ondes avec contrôle frontière contenant un terme intégral.)
Étude d'un problème de transport singulier
Eventual monotonicity and convergence to travelling fronts for the solutions of parabolic equations in cylinders
Evolution by the vortex filament equation of curves with a corner
In this proceedings article we shall survey a series of results on the stability of self-similar solutions of the vortex filament equation. This equation is a geometric flow for curves in and it is used as a model for the evolution of a vortex filament in fluid mechanics. The main theorem give, under suitable assumptions, the existence and description of solutions generated by curves with a corner, for positive and negative times. Its companion theorem describes the evolution of perturbations...
Exact controllability of the wave equation with mixed boundary condition and time-dependent coefficients
In this paper we study the boundary exact controllability for the equation when the control action is of Dirichlet-Neumann form and is a bounded domain in . The result is obtained by applying the HUM (Hilbert Uniqueness Method) due to J. L. Lions.
Existence and Asymptotic Behaviour of Solutions in a System of Reaction Diffusion Equations.
Existence and asymptotic stability for viscoelastic problems with nonlocal boundary dissipation
We consider the damped semilinear viscoelastic wave equation with nonlocal boundary dissipation. The existence of global solutions is proved by means of the Faedo-Galerkin method and the uniform decay rate of the energy is obtained by following the perturbed energy method provided that the kernel of the memory decays exponentially.
Existence and boundary stabilization of a nonlinear hyperbolic equation with time-dependent coefficients.
Existence and boundary stabilization of the semilinear Mindlin-Timoshenko system.
Existence and stability theorems for abstract parabolic equations, and some of their applications
For a class of semi-abstract evolution equations for sections on vector bundles on a three-dimensional compact manifold we prove that for initial values with certain symmetries strong solutions exist for all times. In case these solutions become small after some time, strong solutions exist also for small perturbations of these initial values. Many systems from fluid mechanics are included in this class.
Existence and uniform boundedness of strong solutions of the time-dependent Ginzburg-Landau equations of superconductivity.
Existence and uniqueness of solutions for a semilinear elliptic system.