ABSTRACT
This chapter considers mixed initial-boundary value problems for a specific class of non-linear first order hyperbolic equations, and the functionals of their solutions. Such equations arise in many problems of wave propagation. These are so-called kinematic waves, since the governing equations are obtained from the conservation laws. Examples are flood waves in rivers, waves in glaciers, waves in traffic flow, and certain wave phenomena in chemical reactions. Different functionals of solutions (and especially their deviations from the standard values), which play an important role in these problems, need to be computed. The aim of this chapter is to develop and justify the algorithms for computing the functionals on the basis of adjoint equation technique and perturbation theory.
