The Volterra property of some problems with the Bitsadze–Samarskiĭ-type conditions for a mixed parabolic-hyperbolic equation.
The vortex method for 2D ideal flows in the exterior of a disk
The vortex method is a common numerical and theoretical approach used to implement the motion of an ideal flow, in which the vorticity is approximated by a sum of point vortices, so that the Euler equations read as a system of ordinary differential equations. Such a method is well justified in the full plane, thanks to the explicit representation formulas of Biot and Savart. In an exterior domain, we also replace the impermeable boundary by a collection of point vortices generating the circulation...
The waiting time property for parabolic problems trough the nondiffusion of support for the stationary problems.
In this note we study the waiting time phenomenon for local solutions of the nonlinear diffusion equation through its connection with the nondiffusion of the support property for local solutions of the family of discretized elliptic problems. We show that, under a suitable growth condition on the initial datum near the boundary of its support, a finite part of the family of solutions of the discretized problem maintain unchanged its support.
The warping, the torsion and the Neumann problems in a quasi-periodically perforated domain
The wave equation approach to an inverse eigenvalue problem for an arbitrary multiply connected drum in with Robin boundary conditions.
The wave equation approach to an inverse problem for a general convex domain with impedance boundary conditions
The wave equation with one point interaction and the (linearized) classical electrodynamics of a point particle
The wave equation with oscillating density : observability at low frequency
The wave equation with oscillating density : observability at low frequency
The wave equation with oscillating density: observability at low frequency
We prove an observability estimate for a wave equation with rapidly oscillating density, in a bounded domain with Dirichlet boundary condition.
The Wave Group and Radiation Fields on Asymptotically Hyperbolic Manifolds
The wave map problem. Small data critical regularity
The paper provides a description of the wave map problem with a specific focus on the breakthrough work of T. Tao which showed that a wave map, a dynamic lorentzian analog of a harmonic map, from Minkowski space into a sphere with smooth initial data and a small critical Sobolev norm exists globally in time and remains smooth. When the dimension of the base Minkowski space is , the critical norm coincides with energy, the only manifestly conserved quantity in this (lagrangian) theory. As a consequence,...
The weak Dirichlet and Neumann problem for the Laplacian in for bounded and exterior domains. Applications
The weak type L1 convergence of eigenfunction expansions for pseudodifferential operators.
The well-posedness of a swimming model in the 3-D incompressible fluid governed by the nonstationary Stokes equation
We introduce and investigate the well-posedness of a model describing the self-propelled motion of a small abstract swimmer in the 3-D incompressible fluid governed by the nonstationary Stokes equation, typically associated with low Reynolds numbers. It is assumed that the swimmer's body consists of finitely many subsequently connected parts, identified with the fluid they occupy, linked by rotational and elastic Hooke forces. Models like this are of interest in biological and engineering applications...
The well-posedness of the Dirichlet problem in the cylindric domain for the multidimensional wave equation.
The Weyl asymptotic formula by the method of Tulovskiĭ and Shubin
Let A be a pseudodifferential operator on whose Weyl symbol a is a strictly positive smooth function on such that for some ϱ>0 and all |α|>0, is bounded for large |α|, and . Such an operator A is essentially selfadjoint, bounded from below, and its spectrum is discrete. The remainder term in the Weyl asymptotic formula for the distribution of the eigenvalues of A is estimated. This is done by applying the method of approximate spectral projectors of Tulovskiĭ and Shubin.
The Weyl correspondence as a functional calculus
The aim of this paper is to use an abstract realization of the Weyl correspondence to define functions of pseudo-differential operators. We consider operators that form a self-adjoint Banach algebra. We construct on this algebra a functional calculus with respect to functions which are defined on the Euclidean space and have a finite number of derivatives.
The Wiener criterion and quasilinear uniformly elliptic equations
The Wiener test for degenerate elliptic equations
We consider degenerated elliptic equations of the formUnder suitable assumptions on , we obtain a characterization of Wiener type (involving weighted capacities) for the set of regular points for these operators. The set of regular points is shown to depend only on . The main tool we use is an estimate for the Green function in terms of .