Abstract
This paper deals with the estimation and approximation of 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 by a sequence of solutions of associated finite-dimensional minimization problems.
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Communicated by L. Cesari
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Grasse, K.A., White, L.W. Coefficient estimation in a first-order nonlinear hyperbolic Cauchy problem. J Optim Theory Appl 51, 243–270 (1986). https://doi.org/10.1007/BF00939824
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DOI: https://doi.org/10.1007/BF00939824