On solvability of the Stokes problem in Sobolev power weight spaces
On solving a formal hyperbolic partial differential equation in the complex field.
On some analytical index formulas related to operator-valued symbols.
On some applications of Bogoliubov method for hyperbolic equations
On Some Boundary Element Methods for the Heat Equation.
On some boundary value problems for a class of hyperbolic systems of second order in conic domains.
On some boundary value problems for an ultrahyperbolic equation.
On some boundary value problems for one mixed equation with discontinuous coefficients in a rectangular domain.
On some boundary value problems for systems of nonlinear ordinary differential equations
On some Boussinesq systems in two space dimensions: theory and numerical analysis
A three-parameter family of Boussinesq type systems in two space dimensions is considered. These systems approximate the three-dimensional Euler equations, and consist of three nonlinear dispersive wave equations that describe two-way propagation of long surface waves of small amplitude in ideal fluids over a horizontal bottom. For a subset of these systems it is proved that their Cauchy problem is locally well-posed in suitable Sobolev classes. Further, a class of these systems is discretized...
On some class of quasilinear hyperbolic systems of partial differential-functional equations of the first order
On some classes of linear equations. IV.
On some conjectures by E. De Giorgi relative to the global resolvability of overdetermined systems of differential equations
On some differential inequalities and the uniqueness of global semiclassical solutions to the Cauchy problem for weakly-coupled systems.
On some elliptic boundary-value problems with discontinuous nonlinearities
We establish two existence results for elliptic boundary-value problems with discontinuous nonlinearities. One of them concerns implicit elliptic equations of the form ψ(-Δu) = f(x,u). We emphasize that our assumptions permit the nonlinear term f to be discontinuous with respect to the second variable at each point.
On some elliptic transmission problems
Boundary value problems for second order linear elliptic equations with coefficients having discontinuities of the first kind on an infinite number of smooth surfaces are studied. Existence, uniqueness and regularity results are furnished for the diffraction problem in such a bounded domain, and for the corresponding transmission problem in all of . The transmission problem corresponding to the scattering of acoustic plane waves by an infinitely stratified scatterer, consisting of layers with physically...
On some finite difference schemes for solution of hyperbolic heat conduction problems
We consider the accuracy of two finite difference schemes proposed recently in [Roy S., Vasudeva Murthy A.S., Kudenatti R.B., A numerical method for the hyperbolic-heat conduction equation based on multiple scale technique, Appl. Numer. Math., 2009, 59(6), 1419–1430], and [Mickens R.E., Jordan P.M., A positivity-preserving nonstandard finite difference scheme for the damped wave equation, Numer. Methods Partial Differential Equations, 2004, 20(5), 639–649] to solve an initial-boundary value problem...
On some free boundary problems for Navier-Stokes equations
In this survey we report on existence results for some free boundary problems for equations describing motions of both incompressible and compressible viscous fluids. We also present ways of controlling free boundaries in two cases: a) when the free boundary is governed by surface tension, b) when surface tension does not occur.
On some free boundary problems for the Navier-Stokes equations with moving contact points and lines.
On some fundamental integral inequalities and their discrete analogues.