Unique solvability of the initial boundary value problems for compressible viscous fluids

On the Global Unique Solvability of Initial-Boundary Value Problems for the Coupled Modified Navier–Stokes and Maxwell Equations

The global unique solvability of the first initial-boundary value problem in a bounded, two or three-dimensional domain with fixed perfectly conducting boundaries is proved for the modified Navier–Stokes equations coupled with the Maxwell equations. The system gives a deterministic description of the dynamics for conducting, incompressible, homogeneous fluids. Improved results are proved for th...

Problems in the Theory of Viscous Compressible Fluids

A note on unique solvability of the absolute value equation

It is proved that applying sufficient regularity conditions to the interval matrix $[A-|B|,A + |B|]$, we can create a new unique solvability condition for the absolute value equation $Ax + B|x|=b$, since regularity of interval matrices implies unique solvability of their corresponding absolute value equation. This condition is formulated in terms of positive deniteness of a certain point matrix...

Solvability of Nonlocal Fractional Boundary Value Problems

Solvability of discrete Neumann boundary value problems

In this article we gain solvability to a nonlinear, second-order difference equation with discrete Neumann boundary conditions. Our methods involve new inequalities on the right-hand side of the difference equation and Schaefer’s Theorem in the finite-dimensional space setting. © 2006 Elsevier Inc. All rights reserved.