We establish global regularity results for a wide class of non-linear higher order parabolic systems. The model problem we have in mind is the parabolic p-Laplacian system of order 2m, m≥ 1, ∂tu+(−1) divm (|Dmu|p−2Dmu) = 0 with prescribed boundary and initial values. We prove that if the boundary values are sufficiently regular, then Dmu is globally integrable to a better power than the natural...

We study the Hausdorff dimension spectrum for Lyapunov exponents for a class of interval maps which includes several non-hyperbolic situations. We also analyze the level sets of points with given lower and upper Lyapunov exponents and, in particular, with zero lower Lyapunov exponent. We prove that the level set of points with zero exponent has full Hausdorff dimension, but carries no topologic...

We design a network-based H∞ filter for a parabolic system governed by a vector semilinear N-D diffusion equation over a rectangular domain Ω under distributed in space measurements. The sampled in timemeasurements are sent to the observer over a communication network according to Round-Robin scheduling protocol (one after another in a periodic manner). The objective is to enlarge the sampling ...

We consider elliptic operators with operator-valued coefficients and discuss the associated parabolic problems. The unknowns are functions with values in a Hilbert space W . The system is equipped with a general class of coupled boundary conditions of the form f|∂Ω ∈ Y and ∂f ∂ν ∈ Y⊥, where Y is a closed subspace of L(∂Ω;W ). We discuss well-posedness and further qualitative properties, systema...

Discrete maximum principles are established for finite element approximations 10 of nonlinear parabolic PDE systems with mixed boundary and interface conditions. The 11 results are based on an algebraic discrete maximum principle for suitable ODE systems. 12

A class of triangular parabolic systems given on bounded domains of Rn with arbitrary n is investigated. Sufficient conditions on the structure of the systems are found to assure that weak solutions exist globally.

This study describes the effects of bounce, brake, and roll behavior of a bus toward its leaf spring suspension systems. Parabolic leaf springs are designed based on vertical deflection and stress; however, loads are practically derived from various modes especially under harsh road drives or emergency braking. Parabolic leaf springs must sustain these loads without failing to ensure bus and pa...

Given a family of local systems on the punctured Riemann sphere, its parabolic cohomology is a local system on the base space. We derive exact formulas for the monodromy of this local system. Using the comparison theorem between singular and étale cohomology, we can also (under some conditions) bound its field of moduli. As an application, we prove that the simple groups PSL2(p ) admit regular ...

In this paper we describe a technique that we have used in a number of publications to find the “watershed” under which the initial condition of a positive solution of a nonlinear reaction-diffusion equation must lie, so that this solution does not develop into a traveling wave, but decays into a trivial solution. The watershed consists of the positive solution of the steady-state problem toget...