where Ω is assumed to be a polygonal bounded domain in R2, f ∈ L2(Ω), and α is a bounded function which satisfies the strictly monotone assumption. We estimated the actual error in the H1-norm by an indicator η which is composed of L2norms of the element residual and the jump residual. The main result is divided into two parts; the upper bound and the lower bound for the error. Both of them are...

Two different dynamic inversion compensation schemes for control of nonlinear system with input backlash are presented; one in continuous time and one in discrete time. Both schemes use the backstepping technique with neural networks (NN) for inverting the backlash nonlinearity in the feedforward path. The technique provides a general procedure for using NN to determine the dynamics preinverse ...

We consider continuous-time random walks with bounded jumps but unbounded rates (they depend polynomially on coordinates in the orthant). In applications, the case when the rates are bounded corresponds in applications to queueing theory, more precisely, to Markovian communication networks. The goal of this paper is to discuss the situation for polynomial rates; we show that the boundaries ofte...

We consider fully nonlinear parabolic equations on bounded domains under Dirichlet boundary condition. Assuming that the equation and the domain satisfy certain symmetry conditions, we prove that each bounded positive solution of the Dirichlet problem is asymptotically symmetric. Compared with previous results of this type, we do not assume certain crucial hypotheses, such as uniform (with resp...

In this paper a three stage procedure is presented for deriving parameters bounds of SISOWiener models when the nonlinear block is modeled by a possibly noninvertible polynomial and the output measurement errors are bounded. First, using steady-state input–output data, parameters of the nonlinear part are bounded by a tight orthotope. Then, given the estimated uncertain nonlinearity and the out...

We extend the pseudoholomorphic curve methods from Floer theory to infinite-dimensional phase spaces and use our results prove existence of a forced time-periodic solution general Hamiltonian PDE with regularizing nonlinearity. In particular, when nonlinearity is sufficiently regularizing, bounded time-periodic, we an version Gromov-Floer compactness by using ideas Diophantine approximations ov...

Sampled-data controller is presented for solid oxide fuel cell systems which is expressed by a sector bounded nonlinear model. The proposed control law is obtained by solving a convex problem satisfying several linear matrix inequalities. Simulation results are given to show the effectiveness of the proposed design method. Keywords—Sampled-data control, Sector bound, Solid oxide fuel cell, Time...

This paper deals with the existence of solutions a p-biharmonic pseudo parabolic partial differential equation logarithmic nonlinearity in bounded domain. We prove global weak using Faedo-Galerkin method and applying concavity approach, that blow up at finite time. Further, we provide maximal limit for blow-up

Abstract The long time behaviour of solutions to generalized stochastic porous media equations on bounded intervals with zero Dirichlet boundary conditions is studied. We focus a degenerate form nonlinearity arising in self-organized criticality. Based the so-called lower bound technique, existence and uniqueness an invariant measure proved.