Coefficient estimation in a first-order nonlinear hyperbolic Cauchy problem (Q1067396)

This paper deals with the estimation and approximation of a coefficient function in a first order, nonlinear, hyperbolic Cauchy problem. The estimation is accomplished by minimizing a functional which measures the error between a finite set of given observations and the corresponding values of the solution generated by the coefficient function. A class of admissible coefficient functions is defined, and it is proved that minimizing coefficient function always exists within this class. We also develop an approximation scheme which allows a minimizing coefficient function to be approximated by a sequence of solutions of associated finite-dimensional minimization problems.