— We present recent existence results of quasi-periodic solutions for Schrödinger equations with a multiplicative potential on T , db 1, finitely di¤erentiable nonlinearities, and tangential frequencies constrained along a pre-assigned direction. The solutions have only Sobolev regularity both in time and space. If the nonlinearity and the potential are in Cl then the solutions are in Cl. The p...

Transfer functions models of linear systems are a well established tool for the design and analysis of one-dimensional systems. This is not the case for multidimensional physical systems, given in terms of initial boundary value problems. Here, the only mathematical description of widespread use are partial di erential equations. This contribution shows, how the one-dimensional transfer functio...

The e ciency of numerically solving time-dependent partial di erential equations on parallel computers can be greatly improved by computing the solution on many time-levels simultaneously. The theoretical properties of one such method, namely the discrete-time multigrid waveform relaxation method, are investigated for systems of ordinary di erential equations obtained by spatial nite element di...

The stability in L norm is considered for the Ritz Volterra projection and some applications are presented in this paper As a result point wise error estimates are established for the nite ele ment approximation for the parabolic integro di erential equation Sobolev equations and a di usion equation with non local boundary value problem This work is supported in part by NSERC CANADA Journal of ...

We simulate the Kardar-Parisi-Zhang equation in 2+1 dimensions. It is a non linear stochastic di erential equation which describes driven growing interfaces. The Hopf-Cole transformation is used in order to obtain a stable numerical scheme. The two relevant critical exponents are precisely measured. PACS numbers: 64.60.Ht, 05.40.+j, 05.70.Ln, 68.35.Fx

We synthesize robust nonlinear static output feedback controllers for systems of quasi-linear parabolic partial di!erential equations with time-dependent spatial domains and uncertain variables. The controllers are successfully applied to a typical di!usion}reaction process with moving boundary and uncertainty. ( 2000 Elsevier Science Ltd. All rights reserved.

in this work, we conduct a comparative study among the combine laplace transform and modied adomian decomposition method (lmadm) and two traditional methods for an analytic and approximate treatment of special type of nonlinear volterra integro-differential equations of the second kind. the nonlinear part of integro-differential is approximated by adomian polynomials, and the equation is red...

Since the advent of Taylor Series, polynomial methods have been used to solve di↵erential equations and learn the properties of di↵erential equations. There are many polynomial methods for solving di↵erential equations and understanding dynamical systems. For example, Taylor polynomials, Chebyshev Polynomials and Adomian Polynomials are used to generate approximate solutions. Automatic di↵erent...

We will discuss here Dirichlet problems for non linear …rst order partial di¤erential equations. We will present the recent results of DacorognaMarcellini on this subject; mentioning brie‡y, as a matter of introduction, some results on viscosity solutions.

The problem of learning qualitative models of physical systems from observations of its behaviour has been addressed by several researchers in recent years. Most current techniques limit themselves to learning a single qualitative di erential equation to model the entire system. However, many systems have several qualitative differential equations underlying them. In this paper, we present an a...