Erratum to : “Existence globale et comportement asymptotique pour l'équation de Klein–Gordon quasi linéaire à données petites en dimension 1”
Esistenza e unicità degli stati fondamentali per equazioni ellittiche quasilineari
In this paper we describe some existence and uniqueness theorems for radial ground states of a class of quasilinear elliptic equations. In particular, the mean curvature operator and the degenerate Laplace operator are considered.
Estimates and computations for melting and solidification problems
In this paper we focus on melting and solidification processes described by phase-field models and obtain rigorous estimates for such processes. These estimates are derived in Section 2 and guarantee the convergence of solutions to non-constant equilibrium patterns. The most basic results conclude with the inequality (E2.31). The estimates in the remainder of Section 2 illustrate what obtains if the initial data is progressively more regular and may be omitted on first reading. We also present some...
Estimates and Computations for Melting and Solidification Problems
In this paper we focus on melting and solidification processes described by phase-field models and obtain rigorous estimates for such processes. These estimates are derived in Section 2 and guarantee the convergence of solutions to non-constant equilibrium patterns. The most basic results conclude with the inequality (E2.31). The estimates in the remainder of Section 2 illustrate what obtains if the initial data is progressively more regular and may be omitted on first reading. We also present...
Estimates for Principal Lyapunov Exponents: A Survey
This is a survey of known results on estimating the principal Lyapunov exponent of a timedependent linear differential equation possessing some monotonicity properties. Equations considered are mainly strongly cooperative systems of ordinary differential equations and parabolic partial differential equations of second order. The estimates are given either in terms of the principal (dominant) eigenvalue of some derived time-independent equation or in terms of the parameters of the equation itself....
Estimates for the Asymptotic Behavior of Solutions of the Helmholtz Equation, with an Application to Second order Elliptic Differential Operators with Variable Coefficients.
Estimates for the asymptotic behavior of solutions of the Helmholtz equation, with an application to second order elliptic differential operators with variable coefficients (Erratum).
Estimates near the boundary for second order derivatives of solutions of the Dirichlet problem for the biharmonic equation
Per ogni soluzione della (1) nel dominio limitato ,, appartenente a e soddisfacente le condizioni (2), si dimostra la maggiorazione (5), valida nell'intorno di ogni punto del contorno; si consente a di essere singolare in .
Estimates of a stabilization rate as of solutions of a nonlinear integro-differential equation.
Estimations C1 pour des problèmes paraboliques semi-linéaires
Etude asymptotique de la jonction d'un massif tridimensionnel et d'une tige élancée en flexion.
We are very interested with asymptotic problems for the system of elasticity involving small parameters in the description of the domain where the solutions is searched. The corresponding asymptotic expansions have different forms in the various between them. More precisely, our work is concerned with a precise description of the deformation and the stress fields at the junction of an elastic three-dimensional body and a cylinder. The corresponding small parameter is the diameter of the cylinder....
Étude de la conduction stationnaire dans un domaine comportant une répartition périodique d'inclusions minces de grande conductivité
Étude qualitatif des solutions des équations de Navier-Stokes en dimension 3
Eventual monotonicity and convergence to travelling fronts for the solutions of parabolic equations in cylinders
Evolution in a migrating population model
We consider a model of migrating population occupying a compact domain Ω in the plane. We assume the Malthusian growth of the population at each point x ∈ Ω and that the mobility of individuals depends on x ∈ Ω. The evolution of the probability density u(x,t) that a randomly chosen individual occupies x ∈ Ω at time t is described by the nonlocal linear equation , where φ(x) is a given function characterizing the mobility of individuals living at x. We show that the asymptotic behaviour of u(x,t)...
Evolution of convex entire graphs by curvature flows
We consider the evolution of an entire convex graph in euclidean space with speed given by a symmetric function of the principal curvatures. Under suitable assumptions on the speed and on the initial data, we prove that the solution exists for all times and it remains a graph. In addition, after appropriate rescaling, it converges to a homothetically expanding solution of the flow. In this way, we extend to a class of nonlinear speeds the well known results of Ecker and Huisken for the mean curvature...
Exact controllability of a non-linear generalized damped wave equation: Application to the sine-Gordon equation.
Exact controllability of the wave equation in a thin domain with a wave-like boundary. (Contrôlabilité exacte de l'équation des ondes dans un domaine mince à frontière ondulée.)
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 behavior of boundary blow-up solutions for weighted -Laplacian equations with exponential nonlinearities.