On a weakly hyperbolic quasilinear mixed problem of second order
On a Whitham-type equation.
On ab-initio computations for phase change problems in solids
On acceleration methods for coupled nonlinear elliptic systems.
On additive scharz preconditioners for sparse grid discretizations.
On admissibility for parabolic equations in ℝⁿ
We consider the parabolic equation (P) , (t,x) ∈ ℝ₊ × ℝⁿ, and the corresponding semiflow π in the phase space H¹. We give conditions on the nonlinearity F(x,u), ensuring that all bounded sets of H¹ are π-admissible in the sense of Rybakowski. If F(x,u) is asymptotically linear, under appropriate non-resonance conditions, we use Conley’s index theory to prove the existence of nontrivial equilibria of (P) and of heteroclinic trajectories joining some of these equilibria. The results obtained extend...
On algebraic characterization of coercive linear partial differential operators with constant coefficients
On alternative functional equations. (Short Communication).
On an approximate solution for quasilinear parabolic equations
On an asymptotically linear elliptic Dirichlet problem.
On an elliptic equation with exponential growth
On an embedding criterion for interpolation spaces and application to indefinite spectral problems.
On an equation with partial derivations in four-dimensional Euclidean space.
On an estimate for the linearized compressible Navier-Stokes equations in the -framework
An -estimate with a constant independent of time for solutions of the linearized compressible Navier-Stokes system in the whole space (under the assumption that solutions have compact supports in space) is obtained.
On an estimate for the principal eigenvalue of a linear elliptic problem
On an evolution equation in Banach spaces
On an evolutionary nonlinear fluid model in the limiting case
We consider the two-dimesional spatially periodic problem for an evolutionary system describing unsteady motions of the fluid with shear-dependent viscosity under general assumptions on the form of nonlinear stress tensors that includes those with -structure. The global-in-time existence of a weak solution is established. Some models where the nonlinear operator corresponds to the case are covered by this analysis.
On an existence theorem for the Navier-Stokes equations with free slip boundary condition in exterior domain
This paper deals with a nonstationary problem for the Navier-Stokes equations with a free slip boundary condition in an exterior domain. We obtain a global in time unique solvability theorem and temporal asymptotic behavior of the global strong solution when the initial velocity is sufficiently small in the sense of Lⁿ (n is dimension). The proof is based on the contraction mapping principle with the aid of estimates for the Stokes semigroup associated with a linearized problem, which is also...
On an inequality for a free boundary problem for equations of a viscous compressible heat-conducting capillary fluid
We derive an inequality for a local solution of a free boundary problem for a viscous compressible heat-conducting capillary fluid. This inequality is crucial to proving the global existence of solutions belonging to certain anisotropic Sobolev-Slobodetskiĭ spaces and close to an equilibrium state.
On an inequality in nonlinear thermoelasticity.