Second order nonpersistence of the sine Gordon breather under an exceptional perturbation
Semiclassical measures for the Schrödinger equation on the torus
In this article, the structure of semiclassical measures for solutions to the linear Schrödinger equation on the torus is analysed. We show that the disintegration of such a measure on every invariant lagrangian torus is absolutely continuous with respect to the Lebesgue measure. We obtain an expression of the Radon-Nikodym derivative in terms of the sequence of initial data and show that it satisfies an explicit propagation law. As a consequence, we also prove an observability inequality, saying...
Singly periodic solutions of a semilinear equation
Small time periodic solutions of fully nonlinear telegraph equations in more spatial dimensions
Small time-periodic solutions of equations of magnetohydrodynamics as a singularly perturbed problem
This paper deals with a system of equations describing the motion of viscous electrically conducting incompressible fluid in a bounded three dimensional domain whose boundary is perfectly conducting. The displacement current appearing in Maxwell’s equations, is not neglected. It is proved that for a small periodic force and small positive there exists a locally unique periodic solution of the investigated system. For , these solutions are shown to convergeto a solution of the simplified (and...
Small time-periodic solutions to a nonlinear equation of a vibrating string
In this paper, the system consisting of two nonlinear equations is studied. The former is hyperbolic with a dissipative term and the latter is elliptic. In a special case, the system reduces to the approximate model for the damped transversal vibrations of a string proposed by G. F. Carrier and R. Narasimha. Taking advantage of accelerated convergence methods, the existence of at least one time-periodic solution is stated on condition that the right-hand side of the system is sufficiently small.
Sobre Las Soluciones Periodicas Del Problema De Dirichlet Para Ecuaciones De Tipo Parabolico.
Soluciones Periodicas De Un Modela De Un Reactor Dinamico.
Solution of a linear model of a single-piston pump by means of methods for differential equations in Hilbert spaces
A mathematical model of a fluid flow in a single-piston pump is formulated and solved. Variation of pressure and rate of flow in suction and delivery piping respectively is described by linearized Euler equations for barotropic fluid. A new phenomenon is introduced by a boundary condition with discontinuous coefficient describing function of a valve. The system of Euler equations is converted to a second order equation in the space where is length of the pipe. The existence, unicity and stability...
Solution of a spectral problem for the curl and the Stokes operator with periodic boundary conditions.
Solutions classification to the extended reduced Ostrovsky equation.
Solutions of minimal period of a wave equation via a generalization of a Hofer's theorem
Solutions to three-dimensional Navier-Stokes equations for incompressible fluids.
Soluzioni periodiche di PDEs Hamiltoniane
Presentiamo nuovi risultati di esistenza e molteplicità di soluzioni periodiche di piccola ampiezza per equazioni alle derivate parziali Hamiltoniane. Otteniamo soluzioni periodiche di equazioni «completamente risonanti» aventi nonlinearità generali grazie ad una riduzione di tipo Lyapunov-Schmidt variazionale ed usando argomenti di min-max. Per equazioni «non risonanti» dimostriamo l'esistenza di soluzioni periodiche di tipo Birkhoff-Lewis, mediante un'opportuna forma normale di Birkhoff e realizzando...
Solvability Of Operator Equations And Periodic Solutions Of Semilinear Hyperbolic Equations
Some nonclassical boundary value problems for linear mixed-type equations.
Some topological properties preserved by nearness between operators and applications to P.D.E.
Spatio-Temporal Modelling of the p53–mdm2 Oscillatory System
In this paper we investigate the role of spatial effects in determining the dynamics of a subclass of signalling pathways characterised by their ability to demonstrate oscillatory behaviour. To this end, we formulate a simple spatial model of the p53 network that accounts for both a negative feedback and a transcriptional delay. We show that the formation of protein density patterns can depend on the shape of the cell, position of the nucleus, and the protein diffusion rates. The temporal...
Stabilité en temps grand pour les petites solutions d’équations de Klein-Gordon quasilinéaires sur
Stability of periodic waves in Hamiltonian PDEs
Partial differential equations endowed with a Hamiltonian structure, like the Korteweg–de Vries equation and many other more or less classical models, are known to admit rich families of periodic travelling waves. The stability theory for these waves is still in its infancy though. The issue has been tackled by various means. Of course, it is always possible to address stability from the spectral point of view. However, the link with nonlinear stability - in fact, orbital stability, since we are...