His paper " On the optimality of the observability inequalities for parabolic and hyperbolic systems with potentials ", in collaboration with Thomas Duyckaerts and Xu Zhang, published in Ann.
12.
His Master's thesis " Reflection of Singularities at Boundary for Piecewise Smooth Solutions to Semilinear Hyperbolic Systems " was published in the " Journal of Partial Differential Equations ".
13.
These systems were used well into World War II . By that time, however, radio techniques were becoming much more capable, and most hyperbolic systems are based on radio means.
14.
This is a similar determination as in the case with direct timing / distance measurements, but the hyperbolic system consists of nothing more than a conventional radio receiver hooked to an oscilloscope.
15.
In 1972 DiPerna received from the Courant Institute of Mathematical Sciences his Ph . D . under James Glimm with thesis " Global solutions to a class of nonlinear hyperbolic systems ".
16.
In the case of hyperbolic systems, the notion of weak solution based on distributions does not guarantee uniqueness, and it is necessary to supplement it with entropy conditions or some other selection criterion.
17.
They are constructed on the geometrical structure of stable and unstable manifolds of the dynamical system; they behave physically under small perturbations; and they explain many of the observed statistics of hyperbolic systems.
18.
The accumulated reward at a time " t " can be computed numerically over the time domain or by evaluating the linear hyperbolic system of equations which describe the accumulated reward using transform methods or finite difference methods.
19.
The two-dimensional and three-dimensional wave equations also fall into the category of hyperbolic PDE . This type of second-order hyperbolic partial differential equation may be transformed to a hyperbolic system of first-order differential equations.
20.
Finally it becomes apparent that the real parameter " a " previously defined is the speed of propagation of the information characteristic of the hyperbolic system made of Euler equations, i . e . it is the " wave speed ".
