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The paper considers the inverse problem of determining the unknown coefficient on the righthand side of the hyperbolic equation. An additional condition for finding the unknown coefficient, which depends on the variable time, is given in the integral form. Theorems on the uniqueness, stability, and existence of the solution have been proved. Keywords. Inverse problem, hyperbolic equation, uniqueness, 'conditional' stability, existence., We consider the following inverse problem on determining a pair of function {f(t), u(x, t)} [u.sub.tt] - [u.sub.xx] = f(t)g(x), (x, t) [member of] D = (0, 1) x (0, [...]

The paper considers the inverse problem of determining the unknown coefficient on the right-hand side of the hyperbolic heat equation. An additional condition for finding the unknown coefficient, which depends on the time variable, is given in integral form. Theorems on the uniqueness, stability and existence of the solution are proved. [ABSTRACT FROM AUTHOR]

This paper considers the inverse problem of determining the unknown coefficient on the right-hand side of a parabolic equation in a domain with moving boundaries. An additional condition for finding the unknown coefficient, which depends on the variable time, is given in integral form. A theorem on uniqueness and "conditional" stability of the solution is proved. [ABSTRACT FROM AUTHOR]