Abstract
In this paper, we consider the problem of finding the function , from the final data
and
where is a linear, unbounded, self-adjoint and positive definite operator. This problem is known as the inverse initial problem for non-linear strongly damped wave and is ill-posed in the sense of Hadamard. In order to obtain a stable numerical solution, we propose new quasi-boundary value method to solve the non-linear problem, i.e. for
replacing
by
with the operator will be defined later and
satisfies (1.8). Moreover, we show that the regularized solutions converge to the exact solution strongly with respect to
under a priori assumption on the exact solution in Gevrey space.
Acknowledgements
The authors also desire to thank the handling editor and anonymous referees for their helpful comments on this paper.
Notes
No potential conflict of interest was reported by the authors.