Équations hyperboliques non linéaires
Equations of magnetohydrodynamics of compressible fluid: Periodic solutions
The authors prove the global existence and exponential stability of solutions of the given system of equations under the condition that the initial velocities and the external forces are small and the initial density is not far from a constant one. If the external forces are periodic, then solutions periodic with the same period are obtained. The investigated system of equations is a bit non-standard - for example the displacement current in the Maxwell equations is not neglected.
Equations of mean curvature type on exterior domains.
Equazioni ellittiche non lineari con ostacoli sottili. Applicazioni allo studio dei punti regolari
Equilibrium points for a wave equation with boundary control containing an integral term. (Points d'équilibre pour une équation des ondes avec contrôle frontière contenant un terme intégral.)
Erratum: Geometry of the Rolling Ellipsoid
Erratum to : “Classical solvability in dimension two of the second boundary value problem associated with the Monge–Ampère operator”
Erratum to : “Existence globale et comportement asymptotique pour l'équation de Klein–Gordon quasi linéaire à données petites en dimension 1”
Error estimates on homogenization of free boundary velocities in periodic media
Erweiterung eines Satzes von Serrin über die Gleichungen von Navier-Stokes.
Esistenza e molteplicità di soluzioni per equazioni ellittiche nonlineari
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.
Essential Self-Adjointness of Schrödinger Operators Bounded from Below.
Estimate of the Hausdorff measure of the singular set of a solution for a semi-linear elliptic equation associated with superconductivity
We study the boundedness of the Hausdorff measure of the singular set of any solution for a semi-linear elliptic equation in general dimensional Euclidean space . In our previous paper, we have clarified the structures of the nodal set and singular set of a solution for the semi-linear elliptic equation. In particular, we showed that the singular set is -rectifiable. In this paper, we shall show that under some additive smoothness assumptions, the -dimensional Hausdorff measure of singular set...
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 critical groups of solutions to quasilinear elliptic systems.
Estimates for Evolutionary Surfaces of Prescribed Mean Curvature.
Estimates for hyperbolic equations with non-convex characteristics.
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....