Some modifications of finite-difference schemes for the elliptic singular problem
Some modifications of Sobolev spaces and non-linear boundary value problems
Some modifications of the classic five point finite-difference scheme for the mixed problem for the Laplace equation
Some multiple-part Wiener-Hopf problems in mathematical physics
Some new convergence results in finite element theories for elliptic problems
Some (new) counterexamples of parabolic systems
We give examples of parabolic systems (in space dimension ) having a solution with real analytic initial and boundary values which develops the discontinuity in the interior of the parabolic cylinder.
Some new error estimates for finite element methods for second order hyperbolic equations using the Newmark method
We consider a family of conforming finite element schemes with piecewise polynomial space of degree in space for solving the wave equation, as a model for second order hyperbolic equations. The discretization in time is performed using the Newmark method. A new a priori estimate is proved. Thanks to this new a priori estimate, it is proved that the convergence order of the error is in the discrete norms of and , where and are the mesh size of the spatial and temporal discretization, respectively....
Some new existence results for the variable density Navier-Stokes equations
Some new methods for numerical solution of initial value problems
Some new oscillation criteria for second order elliptic equations with damping
Some new oscillation criteria are obtained for second order elliptic differential equations with damping , x ∈ Ω, where Ω is an exterior domain in ℝⁿ. These criteria are different from most known ones in the sense that they are based on the information only on a sequence of subdomains of Ω ⊂ ℝⁿ, rather than on the whole exterior domain Ω. Our results are more natural in view of the Sturm Separation Theorem.
Some new problems in spectral optimization
We present some new problems in spectral optimization. The first one consists in determining the best domain for the Dirichlet energy (or for the first eigenvalue) of the metric Laplacian, and we consider in particular Riemannian or Finsler manifolds, Carnot-Carathéodory spaces, Gaussian spaces. The second one deals with the optimal shape of a graph when the minimization cost is of spectral type. The third one is the optimization problem for a Schrödinger potential in suitable classes.
Some new problems in the theory of partial differential equations
Some new regularity criteria for the Navier-Stokes equations containing gradient of the velocity
We study the nonstationary Navier-Stokes equations in the entire three-dimensional space and give some criteria on certain components of gradient of the velocity which ensure its global-in-time smoothness.
Some new results in multiphase geometrical optics
Some new results in multiphase geometrical optics
In order to accommodate solutions with multiple phases, corresponding to crossing rays, we formulate geometrical optics for the scalar wave equation as a kinetic transport equation set in phase space. If the maximum number of phases is finite and known a priori we can recover the exact multiphase solution from an associated system of moment equations, closed by an assumption on the form of the density function in the kinetic equation. We consider two different closure assumptions based on delta...
Some new results in spectral and scattering theory of differential operators on
Some new results on a Stefan problem in a concentrated capacity
An existence and uniqueness theorem for a nonlinear parabolic system of partial differential equations, connected with the theory of heat conduction with a transition phase in a concentrated capacity, is given in sufficiently general hypotheses on the data.
Some new results related to the null controllability of the heat equation
We address three null controllability problems related to the heat equation. First we show that the heat equation with a rapidly oscillating density is uniformly null controllable as the period of the density tends to zero. We also prove that the same result holds for the finite-difference semi-discretization in space of the constant coefficient heat equation as the step size tends to zero. Finally, we prove that the null controllability of the constant coefficient heat equation can be obtained...
Some nonclassical boundary value problems for linear mixed-type equations.
Some nonexistence results for higher-order evolution inequalities in cone-like domains.