On the singularities of 3-D Protter's problem for the wave equation.
On the singularities of solutions of partial differential equations with constant coefficients
On the singularities of the solution of the Cauchy problem for the operator with non uniform multiple characteristics
On the Singularities of the Solution to the Cauchy Problem with Singular Data in the Complex Domain.
On the small time asymptotics of the two-dimensional stochastic Navier–Stokes equations
In this paper, we establish a small time large deviation principle (small time asymptotics) for the two-dimensional stochastic Navier–Stokes equations driven by multiplicative noise, which not only involves the study of the small noise, but also the investigation of the effect of the small, but highly nonlinear, unbounded drifts.
On the smallness of the (possible) singular set in space for 3D Navier-Stokes equations.
On the S-matrix for Schrödinger operators with long-range potentials.
On the smoothness of solutions of variational inequalities with obstacles
On the smoothness of the free boundary in a nonlocal one-dimensional parabolic free boundary value problem
We consider one-dimensional parabolic free boundary value problem with a nonlocal (integro-differential) condition on the free boundary. Results on Cm-smoothness of the free boundary are obtained. In particular, a necessary and sufficient condition for infinite differentiability of the free boundary is given.
On the smoothness of the solutions to the elliptic systems
On the smoothness of viscosity solutions of the prescribed Levi-curvature equation
In this paper a -regularity result for the strong viscosity solutions to the prescribed Levi-curvature equation is announced. As an application, starting from a result by Z. Slodkowski and G. Tomassini, the -solvability of the Dirichlet problem related to the same equation is showed.
On the smoothness of weak solutions of strong-nonlinear nondiagonal elliptic systems (the two-dimensional case).
On the solution -dimensional of the product operator and diamond Bessel operator.
On the solution of a generalized system of von Kármán equations
A nonlinear system of equations generalizing von Kármán equations is studied. The existence of a solution is proved and the relation between the solutions of the considered system and the solutions of von Kármán system is studied. The system considered is derived in a former paper by Lepig under the assumption of a nonlinear relation between the intensity of stresses and deformations in the constitutive law.
On the solution of boundary value problems for linear parabolic equations of higher order
On the solution of boundary value problems for sandwich plates
A mathematical model of the equilibrium problem of elastic sandwich plates is established. Using the theory of inequalities of Korn's type for a general class of elliptic systems the existence and uniqueness of a variational solution is proved.
On the solution of elliptic partial differential equations with an unbounded Dirichlet integral
On the solution of indentation and crack problems in linear elasticity by use of higher special functions
On the solution of inverse problems for generalized oxygen consumption
We present the solution of some inverse problems for one-dimensional free boundary problems of oxygen consumption type, with a semilinear convection-diffusion-reaction parabolic equation. Using a fixed domain transformation (Landau’s transformation) the direct problem is reduced to a system of ODEs. To minimize the objective functionals in the inverse problems, we approximate the data by a finite number of parameters with respect to which automatic differentiation is applied.
On the solution of linear algebraic systems arising from the semi–implicit DGFE discretization of the compressible Navier–Stokes equations
We deal with the numerical simulation of a motion of viscous compressible fluids. We discretize the governing Navier–Stokes equations by the backward difference formula – discontinuous Galerkin finite element (BDF-DGFE) method, which exhibits a sufficiently stable, efficient and accurate numerical scheme. The BDF-DGFE method requires a solution of one linear algebra system at each time step. In this paper, we deal with these linear algebra systems with the aid of an iterative solver. We discuss...