Time-periodic scattering of symmetric hyperbolic systems

Safety Verification of Real Time Systems Serving Periodic Devices

In real-time systems response to a request from a controlled object must be correct and timely. Any late response to a request from such a device might lead to a catastrophy. The possibility of a task overrun, i.e., missing the deadline for completing a requested task, must be checked and removed during the design of such systems. Safe design of real-time systems running periodic tasks under th...

Contractive Difference Schemes for Symmetric Hyperbolic Systems

Consider the initial-value problem for a constant-coefficient symmetric hyperbolic system with initial-values vanishing in a half-space. Consider also a finite difference operator consistent with the system. Conditions are given in terms of the orders of dissipation and accuracy which ensure that the solution of the discrete problem tends to zero exponentially with the mesh-width in half-spaces...

Relative Periodic Orbits of Symmetric Lagrangian Systems

Almost Periodic Skew-symmetric Differential Systems

We study solutions of almost periodic linear differential systems. This field is called the Favard theory what is based on the famous Favard result in [10] (see, e.g., [3, Theorem 1.2] or [28, Theorem 1]). It is a well-known corollary of the Favard (and the Floquet) theory that any bounded solution of a periodic linear differential system is almost periodic (see [12, Corollary 6.5] and [13] for...

Computing the Solution Operators of Symmetric Hyperbolic Systems of PDE

We study the computability properties of symmetric hyperbolic systems of PDE A ∂u ∂t + m ∑ i=1 Bi ∂u ∂xi = 0, A = A∗ > 0, Bi = B∗ i , with the initial condition u|t=0 = φ(x1, . . . , xm). Such systems first considered by K.O. Friedrichs can be used to describe a wide variety of physical processes. Using the difference equations approach, we prove computability of the operator that sends (for an...