We extend to the multidimensional case a Wong–Zakai-type theorem proved by Hu and Øksendal (1996) for scalar quasi-linear Itô stochastic differential equations (SDEs). More precisely, with aim of approximating solution quasilinear system Itô’s SDEs, we consider any finite partition time interval [0,T] equations, where Brownian motion is replaced its polygonal approximation product between diffu...

The aim of this article is twofold: (1). develop a strategy to prove the existence of chaos in weakly quasilinear systems, (2). strengthen the existing results on chaos in partial differential equations. First, we study a sineGordon equation containing weakly quasilinear terms, and existence of chaos is proved. Then, we study a Ginzburg-Landau equation containing weakly quasilinear terms, and e...

We consider two models which were both designed to describe the movement of eukaryotic cells responding to chemical signals. Besides a common standard parabolic equation for the diffusion of a chemoattractant, like chemokines or growth factors, the two models differ for the equations describing the movement of cells. The first model is based on a quasilinear hyperbolic system with damping, the ...

We study the dynamics of quasilinear Hamiltonian wave equations with Dirichlet boundary conditions in an n–dimensional parallepided. We prove an averaging theorem according to which the solution corresponding to an arbitrary small amplitude smooth initial datum remains arbitrarily close to a finite dimensional torus up to very long times. We expect the result to be valid for a very general clas...

By means of a result on the semi-global C solution, we establish the exact boundary controllability for the reducible quasilinear hyperbolic system if the C norm of initial data and final state is small enough. Mathematics Subject Classification. 35L50, 49J20, 49N50. Received: October 28, 1999. Revised: November 22, 1999.

We study the Strang splitting scheme for quasilinear Schrödinger equations. We establish the convergence of the scheme for solutions with small initial data. We analyze the linear instability of the numerical scheme, which explains the numerical blow-up of large data solutions and connects to analytical breakdown of regularity of solutions to quasilinear Schrödinger equations. Numerical tests a...

Methods for index reduction of general nonlinear differential-algebraic equations are generally difficult to implement due to the recurring use of functions defined only via the implicit function theorem. By adding structure to the equations, these implicit funcitons may become possible to implement. In particular, this is so for the quasilinear and linear time-invariant (LTI) structures, and i...

Abstract. We consider a system of a semilinear hyperbolic functional differential equation (where the lower order terms contain functional dependence on the unknown functions) with initial and boundary conditions and a quasilinear elliptic functional differential equation (containing t as a parameter) with boundary conditions. Existence of solutions for t ∈ (0, T ) will be shown and some exampl...

Abstract In this paper, we study the Cauchy problems for quasilinear hyperbolic inequalities with nonlocal singular source term and prove nonexistence of global weak solutions in homogeneous nonhomogeneous cases by test function method.

A hydrodynamical model for electron transport in silicon semiconductors, which is free of any fitting parameters, has been formulated on the basis of the maximum entropy principle. The model considers the energy band to be described by the Kane dispersion relation and includes electron–nonpolar optical phonon and electron–acoustic phonon scattering. The set of balance equations of the model for...