We consider global attractors Af of dissipative parabolic equations ut = uxx + f(x; u; ux) on the unit interval 0 x 1 with Neumann boundary conditions. A permutation f is de ned by the two orderings of the set of (hyperbolic) equilibrium solutions ut 0 according to their respective values at the two boundary points x = 0 and x = 1: We prove that two global attractors, Af and Ag, are globally C0...

We consider an optimal stopping problem for a Hilbert-space valued di usion. We prove that the value function of the problem is the unique viscosity solution of an obstacle problem for the associated parabolic partial di erential equation in the Hilbert space. The results are applied to investigate the pricing of American interest rate options in the lognormal Heath-Jarrow-Morton model of yield...

In this survey we recall the results obtained in [16] where we gave a representation theorem for the solutions of stochastic di¤erential equations in Hilbert spaces. Using this representation theorem and the deterministic characterizations of exponential stability and uniform observability obtained in [16], [17], we will prove a result of Datko type concerning the exponential dichotomy of stoch...

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This paper reviews the formulation and application of optimization techniques based on control theory for aerodynamic shape design in both inviscid and viscous compressible ow. The theory is applied to a system de ned by the partial di erential equations of the ow, with the boundary shape acting as the control. The Frechet derivative of the cost function is determined via the solution of an adj...

ABSTRACT: In this paper we brie y describe the interaction of high power laser beam with metal material and its application in the engineering industry. We involve the mathematical model using the nite element method to solve the corresponding partial di erential equation of heat transfer numerically. For application in a laser industry we present results of some examples of heat eld distribution.

We present a scheme for the determination of control Lyapunov functions which can be used as a basis for numerical computations. Under the assumption of local asymptotic nullcontrollability we de ne the domain of asymptotic nullcontrollability. On this set a control Lyapunov function is de ned via an optimal control problem. It is then shown that this function can be characterized as the unique...

Thickeners for solid±liquid separation are still designed and controlled empirically in the mining industry. Great e€orts are being made to develop mathematical models that will change this situation. Starting from the basic principles of continuum mechanics, the authors developed a phenomenological theory of sedimentation for ̄occulated suspensions which takes the compressibility of the ̄ocs u...

Degenerate parabolic equations of Kolmogorov type occur in many areas of analysis and applied mathematics. In their simplest form these equations were introduced by Kolmogorov in 1934 to describe the probability density of the positions and velocities of particles but the equations are also used as prototypes for evolution equations arising in the kinetic theory of gases. More recently equation...

We address the enumeration of q-coloured planar maps counted by the number of edges and the number of monochromatic edges. We prove that the associated generating function is di erentially algebraic, that is, satis es a non-trivial polynomial di erential equation with respect to the edge variable. We give explicitly a di erential system that characterizes this series. We then prove a similar re...