Consider a random environment in given by i.i.d. conductances. In this work, we obtain tail estimates for the fluctuations about the mean for the following characteristics of the environment: the effective conductance between opposite faces of a cube, the diffusion matrices of periodized environments and the spectral gap of the random walk in a finite cube.
The a priori estimate of the maximum modulus of the generalized solution is established for a doubly nonlinear parabolic equation with special structural conditions.
This paper deals with blow-up properties of solutions to a semilinear parabolic system with weighted localized terms, subject to the homogeneous Dirichlet boundary conditions. We investigate the influence of the three factors: localized sources , vⁿ(x₀,t), local sources , , and weight functions a(x),b(x), on the asymptotic behavior of solutions. We obtain the uniform blow-up profiles not only for the cases m,q ≤ 1 or m,q > 1, but also for m > 1 q < 1 or m < 1 q > 1.
We study the anti-disturbance problem of a 1-d wave equation with boundary control matched disturbance. In earlier literature, the authors always designed the controller such as the sliding mode control and the active disturbance rejection control to stabilize the system. However, most of the corresponding closed-loop systems are boundedly stable. In this paper we show that the linear feedback control also has a property of anti-disturbance, even if the disturbance includes some information of the...
In this paper, we study how solutions to elliptic problems with periodically oscillating coefficients behave in the neighborhood of the boundary of a domain. We extend the results known for flat boundaries to domains with curved boundaries in the case of a layered medium. This is done by generalizing the notion of boundary layer and by defining boundary correctors which lead to an approximation of order in the energy norm.
In this paper, we study how solutions to elliptic problems with periodically oscillating coefficients behave in the neighborhood of the boundary of a domain. We extend the results known for flat boundaries to domains with curved boundaries in the case of a layered medium. This is done by generalizing the notion of boundary layer and by defining boundary correctors which lead to an approximation of order ε in the energy norm.
We assume that is a weak solution to the non-steady Navier-Stokes initial-boundary value problem that satisfies the strong energy inequality in its domain and the Prodi-Serrin integrability condition in the neighborhood of the boundary. We show the consequences for the regularity of near the boundary and the connection with the interior regularity of an associated pressure and the time derivative of .
Dirac-harmonic maps are a mathematical version (with commuting variables only) of the solutions of the field equations of the non-linear supersymmetric sigma model of quantum field theory. We explain this structure, including the appropriate boundary conditions, in a geometric framework. The main results of our paper are concerned with the analytic regularity theory of such Dirac-harmonic maps. We study Dirac-harmonic maps from a Riemannian surface to an arbitrary compact Riemannian manifold. We...