Abstract
Let Ω be a bounded domain of with smooth boundary,
,
and let
be a self-adjoint operator defined on a dense subspace
such that A has an orthonormal basis of eigenfunctions in
. For Y >0, giving the function
, we consider the problem of finding a function
such that
In the system, the function
is unknown and approximated by a given function
such that
for a
small. This Cauchy problem is ill-posed and has many applications in physics and other fields. For this reason, a regularization for the problem is in order.
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Acknowledgments
The authors would like to thank the anonymous referee for constructive criticisms leading to the improvement of our paper. The paper is supported by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.02-2019.321.
Disclosure statement
No potential conflict of interest was reported by the authors.