On nonlinear superposition, III.
On perturbative cubic nonlinear Schrödinger equations under complex nonhomogeneities and complex initial conditions.
On pressure boundary conditions for steady flows of incompressible fluids with pressure and shear rate dependent viscosities
We consider a class of incompressible fluids whose viscosities depend on the pressure and the shear rate. Suitable boundary conditions on the traction at the inflow/outflow part of boundary are given. As an advantage of this, the mean value of the pressure over the domain is no more a free parameter which would have to be prescribed otherwise. We prove the existence and uniqueness of weak solutions (the latter for small data) and discuss particular applications of the results.
On Pseudo-monotone Operators and Nonlinear Noncoercive Variational Problems on Unbounded Domains.
On quasiconvex equimeasurable rearrangement, a counterexample and an example.
On quasilinear elliptic equations in .
On reflection of shock front in multidimensional space
On second order Hamiltonian systems
The aim of the paper is to announce some recent results concerning Hamiltonian theory. The case of second order Euler–Lagrange form non-affine in the second derivatives is studied. Its related second order Hamiltonian systems and geometrical correspondence between solutions of Hamilton and Euler–Lagrange equations are found.
On set-valued non-Boolean functions.
On Signorini problem for von Kármán equations
On smoothness of a fundamental solution to a second order hyperbolic equation.
On some applications of Bogoliubov method for hyperbolic equations
On some quasimetrics and their applications.
On source terms and boundary conditions using arbitrary high order discontinuous Galerkin schemes
This article is devoted to the discretization of source terms and boundary conditions using discontinuous Galerkin schemes with an arbitrary high order of accuracy in space and time for the solution of hyperbolic conservation laws on unstructured triangular meshes. The building block of the method is a particular numerical flux function at the element interfaces based on the solution of Generalized Riemann Problems (GRPs) with piecewise polynomial initial data. The solution of the generalized Riemann...
On spectral properties of the Laplace operator via boundary perturbation.
On splitting up singularities of fundamental solutions to elliptic equations in ℂ2
It is known that the fundamental solution to an elliptic differential equation with analytic coefficients exists, is determined up to the kernel of the differential operator, and has singularities on characteristics of the equation in ℂ2. In this paper we construct a representation of fundamental solution as a sum of functions, each of those has singularity on a single characteristic.
On stabilizability of evolution systems of partial differential equations on ℝn×[0,+∞) by time-delayed feedback controlsby time-delayed feedback controls
On stabilization and control for the critical Klein-Gordon equation on a 3-D compact manifold
We study the internal stabilization and control of the critical nonlinear Klein-Gordon equation on 3-D compact manifolds. Under a geometric assumption slightly stronger than the classical geometric control condition, we prove exponential decay for some solutions bounded in the energy space but small in a lower norm. The proof combines profile decomposition and microlocal arguments. This profile decomposition, analogous to the one of Bahouri-Gérard [2] on , is performed by taking care of possible...
On the angle condition for the perturbation of elliptic systems
On the approximation of elliptic operators with discontinuous coefficients