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In this paper, we consider the existence of a solution  u ( x ,  t ) for the inverse backward problem for the nonlinear strongly damped wave equation with statistics discrete data. The problem is severely ill-posed in the sense of Hadamard, i.e., the solution does not depend continuously on the data. In order to regularize the unstable solution, we use the trigonometric method in non-parametric regression associated with the truncated expansion method. We investigate the convergence rate under some  a priori  assumptions on an exact solution in both  L   2  and  Hq    ( q  &gt; 0) norms. Moreover, a numerical example is given to illustrate our results.

On the inverse problem for nonlinear strongly damped wave equations with discrete random noise