On a shock problem involving a nonlinear viscoelastic bar.
On an approximate solution for quasilinear parabolic equations
On evolution Galerkin methods for the Maxwell and the linearized Euler equations
The subject of the paper is the derivation and analysis of evolution Galerkin schemes for the two dimensional Maxwell and linearized Euler equations. The aim is to construct a method which takes into account better the infinitely many directions of propagation of waves. To do this the initial function is evolved using the characteristic cone and then projected onto a finite element space. We derive the divergence-free property and estimate the dispersion relation as well. We present some numerical...
On iterative solution of nonlinear heat-conduction and diffusion problems
The present paper deals with the numerical solution of the nonlinear heat equation. An iterative method is suggested in which the iterations are obtained by solving linear heat equation. The convergence of the method is proved under very natural conditions on given input data of the original problem. Further, questions of convergence of the Galerkin method applied to the original equation as well as to the linear equations in the above mentioned iterative method are studied.
On reflection of shock front in multidimensional space
On some applications of Bogoliubov method for hyperbolic equations
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 the angle condition for the perturbation of elliptic systems
On the Chaplighin method for partial differential equations of the first order
On the convergence of numerical schemes for the Boltzmann equation
On the Dirichlet problem for a second order elliptic system with degeneration on the entire domain boundary.
On the existence and uniqueness of solutions of some partial differential functional equations
On the existence and uniqueness of solutions of the Darboux problem for partial differential-functional equations in a Banach space
On the existence of weak solutions of perturbated systems with critical growth.
On the Landau approximation in plasma physics
On the non-convergence of successive approximations in the Darboux problem for the equation
On the nonconvergence of successive approximations in the theory of the equation
On the -growth of entire function solutions of Helmholtz equation.
On the relation between the Maslov-Whitham method and the weak asymptotics method
We explain the relation between the weak asymptotics method introduced by the author and V. M. Shelkovich and the classical Maslov-Whitham method for constructing approximate solutions describing the propagation of nonlinear solitary waves.