An inverse problem for a general doubly-connected bounded domain with impedance boundary conditions.
An inverse problem for a nonlinear Schrödinger equation.
An inverse problem for a second-order differential equation in a Banach space.
An inverse problem for evolution inclusions.
An inverse problem for Helmholtz's equation.
An inverse problem for the equation
Let be a bounded, convex planar domain whose boundary has a not too degenerate curvature. In this paper we provide partial answers to an identification question associated with the boundary value problemWe prove two results: 1) If is not a ball and if one considers only solutions with , then there exist at most finitely many pairs of coefficients so that the normal derivative equals a given .2) If one imposes no sign condition on the solutions but one additionally supposes that is sufficiently...
An inverse problem for time-harmonic electromagnetic currents in a smoothly layered medium.
An inverse problem in a parabolic equation.
An inverse problem of the wave equation.
An inversion of the obstacle problem and its explicit solution
An -theory of existence and uniqueness of solutions of nonlinear elliptic equations
An operatorial approach to stochastic partial differential equations driven by linear multiplicative noise
An optimal estimate for the singular set of a harmonic map in the free boundary.
An overlapping additive Schwarz-Richardson method for monotone nonlinear parabolic problems.
An upper bound on the attractor dimension of a 2D turbulent shear flow with a free boundary condition
We consider a free boundary problem of a two-dimensional Navier-Stokes shear flow. There exist a unique global in time solution of the considered problem as well as the global attractor for the associated semigroup. As in [1] and [2], we estimate from above the dimension of the attractor in terms of given data and the geometry of the domain of the flow. This research is motivated by a free boundary problem from lubrication theory where the domain of the flow is usually very thin and the roughness...
Análisis de las singularidades de una ecuación diferencial fraccionaria no lineal.
Se exponen las estimaciones numéricas preliminares de las singularidades de una ecuación diferencial fraccionaria no lineal. Dicha ecuación aparece en el estudio de las ondas viajeras asociadas a una ecuación de ondas que es una interpolación entre la ecuación de ondas clásica y la ecuación de Benjamin-Ono.
Analyse harmonique non linéaire
Analysis of Hamilton-Jacobi-Bellman equations arising in stochastic singular control
We study the partial differential equation max{Lu − f, H(Du)} = 0 where u is the unknown function, L is a second-order elliptic operator, f is a given smooth function and H is a convex function. This is a model equation for Hamilton-Jacobi-Bellman equations arising in stochastic singular control. We establish the existence of a unique viscosity solution of the Dirichlet problem that has a Hölder continuous gradient. We also show that if H is uniformly convex, the gradient of this solution...
Analysis of the boundary symbol for the two-phase Navier-Stokes equations with surface tension
The two-phase free boundary value problem for the Navier-Stokes system is considered in a situation where the initial interface is close to a halfplane. We extract the boundary symbol which is crucial for the dynamics of the free boundary and present an analysis of this symbol. Of particular interest are its singularities and zeros which lead to refined mapping properties of the corresponding operator.
Analysis of the free boundary for the p-parabolic variational problem (p ≥ 2).
Abstract Variational inequalities (free boundaries), governed by the p-parabolic equation (p > 2), are the objects of investigation in this paper. Using intrinsic scaling we establish the behavior of solutions near the free boundary. A consequence of this is that the time levels of the free boundary are porous (in N-dimension) and therefore its Hausdorff dimension is less than N. In particular the N-Lebesgue measure of the free boundary is zero for each t-level.