AN INVERSE PROBLEM FOR THE PSEUDO-PARABOLIC EQUATION FOR A STURM-LIOUVILLE OPERATOR
Ключевые слова:
Pseudo-parabolic equation, Sturm-Liouville operator, fractional Caputo derivative, inverse problem, well-posedness.Аннотация
A class of inverse problems for restoring the right-hand side of the pseudo-parabolic equation for
Sturm–Liouville operator is considered. The inverse problem is to be well-posed in the sense of Hadamard whenever
an overdetermination condition of the final temperature is given. Mathematical statements involve inverse problems
for the pseudo-parabolic equation in which, solving the equation, we have to find the unknown right-hand side
depending only on the space variable. We prove the existence and uniqueness of classical solutions to the problem.
The proof of the existence and uniqueness results of the solutions is carried out by using L-Fourier analysis. The
mentioned results are presented as well as for the fractional time pseudo–parabolic equation.Inverse problem of
identifying the right hand side function of pseudo-parabolic equation from the local overdetermination condition,
which has important applications in various areas of applied science and engineering, alsosuch problems are
modeled using common homogeneous left-invariant hypoelliptic operators on common graded Lie groups.
