On the Yang-Mills heat equation in two and three dimensions.
On the -convergence of Laplace-Beltrami operators in the plane.
On uniqueness and stability of steady-state carrier distributions in semiconductors
Ondes oscillantes semi-linéaires en 1.d
Optimal energy decay rate of coupled wave equations.
Optimization problems for structural acoustic models with thermoelasticity and smart materials
Optimization problem for a structural acoustic model with controls governed by unbounded operators on the state space is considered. This type of controls arises naturally in the context of "smart material technology". The main result of the paper provides an optimal synthesis and solvability of associated nonstandard Riccati equations. It is shown that in spite of the unboundedness of control operators, the resulting gain operators (feedbacks) are bounded on the state space. This allows to provide...
Optique géométrique oscillante en présence d'un grand choc
Orbital stability for polytropic galaxies
Oscillations of a nonlinearly damped extensible beam
It is proved that any weak solution to a nonlinear beam equation is eventually globally oscillatory, i.e., there is a uniform oscillatory interval for large times.
Otto Vejvoda passed away
Parabolic boundary-value problems with equivalued surface on the domain with a thin layer.
Parabolic partial differential equations with memory
Partly dissipative systems in uniformly local spaces
We study the existence of attractors for partly dissipative systems in ℝⁿ. For these systems we prove the existence of global attractors with attraction properties and compactness in a slightly weaker topology than the topology of the phase space. We obtain abstract results extending the usual theory to encompass such two-topologies attractors. These results are applied to the FitzHugh-Nagumo equations in ℝⁿ and to Field-Noyes equations in ℝ. Some embeddings between uniformly local spaces are also...
PDE models for chemotactic movements: Parabolic, hyperbolic and kinetic
Modeling the movement of cells (bacteria, amoeba) is a long standing subject and partial differential equations have been used several times. The most classical and successful system was proposed by Patlak and Keller & Segel and is formed of parabolic or elliptic equations coupled through a drift term. This model exhibits a very deep mathematical structure because smooth solutions exist for small initial norm (in the appropriate space) and blow-up for large norms. This reflects experiments on...
Periodic solutions of a three-species periodic reaction-diffusion system
We study a periodic reaction-diffusion system of a competitive model with Dirichlet boundary conditions. By the method of upper and lower solutions and an argument similar to that of Ahmad and Lazer, we establish the existence of periodic solutions and also investigate the stability and global attractivity of positive periodic solutions under certain conditions.
Phase transition with supercooling
L'articolo riassume il quadro dei risultati noti circa il cosiddetto problema di Stefan con sopraraffreddamento. Con ciò si intende in senso lato l'estensione del modello di Stefan a quei casi in cui la temperatura della fase liquida (solida) non è confinata al di sopra (sotto) di quella di cambiamento di fase, supposta costante. La nostra discussione è prevalentemente rivolta allo sviluppo di singolarità (non limitatezza della velocità dell'interfaccia, ecc.), al modo di prevederle, di prevenirle...
Poincaré theorem and nonlinear PDE's
A family of formal solutions of some type of nonlinear partial differential equations is found. Terms of such solutions are Laplace transforms of some Laplace distributions. The series of these distributions are locally finite.
Pointwise bounds for solutions of the equation - ...v + pv = 0.
Polynomial boundedness of eigensolutions and the spectrum of Schrödinger operators.
Positive solutions for a class of quasilinear singular equations.