Existence de solutions non bornées pour certaines équations quasi-linéaires
Existence of global solutions for a predator-prey model with cross-diffusion.
Existence of stable periodic solutions for quasilinear parabolic problems in the presence of well-ordered lower and upper-solutions.
Existence of stable periodic solutions of a semilinear parabolic problem under Hammerstein-type conditions.
Existence of threedimensional, steady, inviscid, incompressible flows with nonvanishing vorticity.
Existence, uniqueness and stability for spatially inhomogeneous Becker-Döring equations with diffusion and convection terms
We consider the spatially inhomogeneous Bekker-Döring infinite-dimensional kinetic system describing the evolution of coagulating and fragmenting particles under the influence of convection and diffusion. The simultaneous consideration of opposite coagulating and fragmenting processes causes many additional difficulties in the investigation of spatially inhomogeneous problems, where the space variable changes differently for distinct particle sizes. To overcome these difficulties, we use a modified...
Existencia De Multiples Soluciones De Un Problema Eliptico Con Parte Lineal En Resonancia Con El Primer Valor Propio.
Explicit bounds on some nonlinear integral inequalities.
Explosion pour l’équation de Schrödinger au régime du “log log”
On présente dans cet exposé des résultats récents de Merle et Raphael sur l’analyse des solutions explosives de l’équation de Schrödinger critique. On s’intéresse en particulier à leur preuve du fait que les solutions d’énergie négative (dont on savait qu’elles explosaient par l’argument du viriel) et dont la norme est proche de celle de l’état fondamental, explosent au régime du “log log”et que ce comportement est stable.
Exponential decay of solutions to a viscoelastic equation with nonlinear localized damping.
Exponential stability conditions for non-autonomous differential equations with unbounded commutators in a Banach space
We consider the equation , where is the generator of an analytic semigroup on a Banach space , is a variable bounded operator in . It is assumed...
Exponential stability for impulsive BAM neural networks with time-varying delays and reaction-diffusion terms.
Exponential stability for the wave equation with weak nonmonotone damping.
Extremal equilibria for parabolic non-linear reaction-diffusion equations
Feedback stabilization of semilinear heat equations.
Free boundary problems and transonic shocks for the Euler equations in unbounded domains
We establish the existence and stability of multidimensional transonic shocks (hyperbolic-elliptic shocks), which are not nearly orthogonal to the flow direction, for the Euler equations for steady compressible potential fluids in unbounded domains in . The Euler equations can be written as a second order nonlinear equation of mixed hyperbolic-elliptic type for the velocity potential. The transonic shock problem can be formulated into the following free boundary problem: The free boundary is the...
Free boundary problems arising in tumor models
We consider several simple models of tumor growth, described by systems of PDEs, and describe results on existence of solutions and on their asymptotic behavior. The boundary of the tumor region is a free boundary. In §1 the model assumes three types of cells, proliferating, quiescent and necrotic, and the corresponding PDE system consists of elliptic, parabolic and hyperbolic equations. The model in §2 assumes that the tumor has only proliferating cells. Finally in §3 we consider a model for treatment...
Free-energy-dissipative schemes for the Oldroyd-B model
In this article, we analyze the stability of various numerical schemes for differential models of viscoelastic fluids. More precisely, we consider the prototypical Oldroyd-B model, for which a free energy dissipation holds, and we show under which assumptions such a dissipation is also satisfied for the numerical scheme. Among the numerical schemes we analyze, we consider some discretizations based on the log-formulation of the Oldroyd-B system proposed by Fattal and Kupferman in [J. Non-Newtonian...
Generalized Functions Solutions of Monotone and Semilinear Parabolic Equations.
Generalized solutions to hybrid dynamical systems
Several recent results in the area of robust asymptotic stability of hybrid systems show that the concept of a generalized solution to a hybrid system is suitable for the analysis and design of hybrid control systems. In this paper, we show that such generalized solutions are exactly the solutions that arise when measurement noise in the system is taken into account.