Numerical Solution of a Hyperbolic Free Boundary Problem with a Method of Characteristics.
On 3D slightly compressible Euler equations.
On a mixed boundary values problem for Lavrentev type equations
On a new superposition principle for optimization problem
On Maxwell equations with the Preisach hysteresis operator: The one- dimensional time-periodic case
Energy functionals for the Preisach hysteresis operator are used for proving the existence of weak periodic solutions of the one-dimensional systems of Maxwell equations with hysteresis for not too large right-hand sides. The upper bound for the speed of propagation of waves is independent of the hysteresis operator.
On nonlinear Schrödinger equations
On nonviscous compressible fluids in a time-dependent domain
On some applications of Bogoliubov method for hyperbolic equations
On some class of quasilinear hyperbolic systems of partial differential-functional equations of the first order
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 the anomalous singularities of the solutions to some classes of weakly hyperbolic semilinear systems. Examples
This paper deals with the newly observed singularities of the solutions of some specific examples of weakly hyperbolic semilinear systems in R². Two, respectively three, characteristics are supposed to be mutually tangential at the origin only and the initial data are continuous only. The exact strength of the new-born singularities is investigated too.
On the barotropic motion of compressible perfect fluids
On the behaviour of generalized solutions to genuinely nonlinear first order equations for small and large values of time.
The paper deals with the asymptotic behavior of generalized solutions to nonlinear first order equations. With the aid of explicit variational representation one studies the decrease of solutions for a large time. And for the small time an asymptotic of the perturbation?s front is calculated.
On the Cauchy problem for the equations of ideal compressible MHD fluids with radiation
We consider a system of balance laws describing the motion of an ionized compressible fluid interacting with magnetic fields and radiation effects. The local-in-time existence of a unique smooth solution for the Cauchy problem is proven. The proof follows from the method of successive approximations.
On the effect of temperature and velocity relaxation in two-phase flow models
We study a two-phase pipe flow model with relaxation terms in the momentum and energy equations, driving the model towards dynamic and thermal equilibrium. These equilibrium states are characterized by the velocities and temperatures being equal in each phase. For each of these relaxation processes, we consider the limits of zero and infinite relaxation times. By expanding on previously established results, we derive a formulation of the mixture sound velocity for the thermally relaxed model. This...
On the effect of temperature and velocity relaxation in two-phase flow models
We study a two-phase pipe flow model with relaxation terms in the momentum and energy equations, driving the model towards dynamic and thermal equilibrium. These equilibrium states are characterized by the velocities and temperatures being equal in each phase. For each of these relaxation processes, we consider the limits of zero and infinite relaxation times. By expanding on previously established results, we derive a formulation of the mixture sound velocity for the thermally relaxed model. This...
On the equations of ideal incompressible magneto-hydrodynamics
On the Existence of Generalized Solutions and the Convergence of Difference Methods for Nonlinear Initial-Value Problems.
On the existence of weak solutions for a semilinear singular hiperbolic system.
In this paper we prove the existence of a weak solution for a given semilinear singular real hyperbolic system.
On the local Cauchy problem for nonlinear hyperbolic functional differential equations
We consider the local initial value problem for the hyperbolic partial functional differential equation of the first order (1) on E, (2) z(x,y) = ϕ(x,y) on [-τ₀,0]×[-b,b], where E is the Haar pyramid and τ₀ ∈ ℝ₊, b = (b₁,...,bₙ) ∈ ℝⁿ₊. Using the method of bicharacteristics and the method of successive approximations for a certain functional integral system we prove, under suitable assumptions, a theorem on the local existence of weak solutions of the problem (1),(2).