Inverse source problems for time-fractional mixed parabolic-hyperbolic type equations

摘要

In the present paper we consider an inverse source problem fortime-fractional mixed parabolic-hyperbolic equation with the Caputo derivative.In case, when hyperbolic part of the considered mixed type equation is waveequation, the uniqueness of source and solution are strongly influenced byinitial time and generally is ill-posed. However, when the hyperbolic part istime fractional, the problem is well posed if end time is large. Our methodrelies on the orthonormal system of eigenfunctions of the operator with respectto space variable. We proved the uniqueness and stability of certain weaksolutions for considered problems.