Which solutions of the third problem for the Poisson equation are bounded?
Whitham averaged equations and modulational stability of periodic traveling waves of a hyperbolic-parabolic balance law
In this note, we report on recent findings concerning the spectral and nonlinear stability of periodic traveling wave solutions of hyperbolic-parabolic systems of balance laws, as applied to the St. Venant equations of shallow water flow down an incline. We begin by introducing a natural set of spectral stability assumptions, motivated by considerations from the Whitham averaged equations, and outline the recent proof yielding nonlinear stability under these conditions. We then turn to an analytical...
Wiener criterion for degenerate elliptic obstacle problem
We give a Wiener criterion for the continuity of an obstacle problem relative to an elliptic degenerate problem with a weight in the class.
WKB analysis for the Gross-Pitaevskii equation with non-trivial boundary conditions at infinity
Worst scenario method in homogenization. Linear case
The paper deals with homogenization of a linear elliptic boundary problem with a specific class of uncertain coefficients describing composite materials with periodic structure. Instead of stochastic approach to the problem, we use the worst scenario method due to Hlaváček (method of reliable solution). A few criterion functionals are introduced. We focus on the range of the homogenized coefficients from knowledge of the ranges of individual components in the composite, on the values of generalized...