Table of contents
The accuracy of Dafermos' method for nonlinear hyperbolic equations
The accuracy of numerically computed orbits of dynamical systems
The asymptotic behavior at the large time of solutions of some mathematical physics problems
The box method and some error estimation
This article focuses its attention on practical use of the box method for solving certain type of partial differential equations. The heat conduction problem of the oil transformer under stationary load is described by this equation. The knowledge of the transformer operating temperature is important for ensuring correct functionality and lifespan of transformer. We consider an elliptic partial differential equation of second order with the Newton boundary condition on a rectangular domain. The...
The dimension of a set of singularities of weak solutions to the Navier-Stokes equations
The Dirichlet problem
The Dirichlet problem for sublaplacians on nilpotent Lie groups - geometric criteria for regularity
The geometric theory of Volterra integral equations - a preliminary report
The global solvability to the equations of motion of viscous gas with an artificial viscosity
The Helmholtz decomposition and the weak Neumann problem in
The method of discretization in time and partial differential equations
The method of least squares on the boundary and very weak solutions of the first biharmonic problem
The numerical solution of compressible flows in time dependent domains
This work is concerned with the numerical solution of inviscid compressible fluid flow in moving domains. Specifically, we assume that the boundary part of the domain (impermeable walls) are time dependent. We consider the Euler equations, which describe the movement of inviscid compressible fluids. We present two formulations of the Euler equations in the ALE (Arbitrary Lagrangian-Eulerian) form. These two formulations are discretized in space by the discontinuous Galerkin method. We apply a semi-implicit linearization...
The optimal control problem in coefficients for the pseudoparabolic variational inequality
The periodic boundary value problem for some second order ordinary differential equations
The Rayleigh and van der Pol wave equations, some generalizations
The role of center manifolds in ordinary differential equations
The solution of parabolic models by finite element space and -stable time discrezation
The solution of the initial value problem for the general dynamic equations in nonlinear elasticity under damping conditions