Boundedness and monotonicity of principal eigenvalues for boundary value problems with indefinite weight functions.
Boundedness of Solutions of Non-Linear Differential Equation Systems
Boundedness of two- and three-body resonances
Burgers' equation with nonlinear boundary feedback: stability, well-posedness and simulation.
Cloaking via anomalous localized resonance for doubly complementary media in the quasistatic regime
This paper is devoted to the study of cloaking via anomalous localized resonance (CALR) in the two- and three-dimensional quasistatic regimes. CALR associated with negative index materials was discovered by Milton and Nicorovici [21] for constant plasmonic structures in the two-dimensional quasistatic regime. Two key features of this phenomenon are the localized resonance, i.e., the fields blow up in some regions and remain bounded in some others, and the connection between the localized resonance...
Coexistence and stability of solutions for a class of reaction-diffusion systems.
Comportement à l'infini des solutions des équations de Navier-Stokes et propriété des ensembles fonctionnels invariants (ou attracteurs)
Les données, i.e. l’ouvert et la force appliquée , sont supposées de classe . Il est montré que toute solution des équations de Navier-Stokes dans l’ouvert , bornée dans ( ou ) sur un intervalle de temps semi-infini , est aussi bornée, pour , dans tous les espaces . Il en résulte que tout ensemble fonctionnel invariant ou attracteur borné dans (ou même , ) est porté par . Le cas où les forces appliquées dérivent d’un potentiel (i.e. ) est abordé : il est montré que toute solution...
Comportement asymptotique des solutions des équations de type Schrödinger dans
Condition nécessaire d'optimalité pour un système régi par des équations aux dérivés partielles non linéaires de type parabolique
Continuous dependence and stability for non linear dispersive and dissipative waves
Continuous host-macroparasite models with application to aquaculture.
Contrôle et stabilisation hyperboliques
Controllable systems of partial differential equations
In the paper definitions of various kinds of stability and boundedness of solutions of linear controllable systems of partial differential equations are introduced and their interconnections are derived. By means of Ljapunov's functions theorems are proved which give necessary and sufficient conditions for particular kinds of stability and boundedness of the solutions.
Convergence results for unbounded solutions of first order non-linear differential-functional equations
We consider the Cauchy problem in an unbounded region for equations of the type either or . We prove convergence of their difference analogues by means of recurrence inequalities in some wide classes of unbounded functions.
Corner defects in almost planar interface propagation
Counterexample to the regularity of weak solution of the quasilinear parabolic system
Counterexamples for Uniqueness in Strongly Coupled Parabolic Systems.
Destabilization for quasivariational inequalities of reaction-diffusion type
We consider a reaction-diffusion system of the activator-inhibitor type with unilateral boundary conditions leading to a quasivariational inequality. We show that there exists a positive eigenvalue of the problem and we obtain an instability of the trivial solution also in some area of parameters where the trivial solution of the same system with Dirichlet and Neumann boundary conditions is stable. Theorems are proved using the method of a jump in the Leray-Schauder degree.
Destabilizing effect of unilateral conditions in reaction-diffusion systems
Diffusion and cross-diffusion in pattern formation
We discuss the stability and instability properties of steady state solutions to single equations, shadow systems, as well as systems. Our basic observation is that the more complicated the pattern are, the more unstable they tend to be.