Determination of a nonlinear coefficient in a hyperbolic equation for the Goursat problem

Abstract

We consider an inverse problem for a nonlinear hyperbolic equation with an unknown coefficient which depends on the solution of the equation. A theorem of uniqueness of solution to this inverse problem is proved.

A generalized integral problem for a system of hyperbolic equations and its applications

“…By introducing the additional functional parameters, the considered problem was transformed to an equivalent problem, consisting of the Goursat problem for a system of hyperbolic equations with unknown parameters and functional relations. Note, that the resulting equivalent problem can be seen as the inverse nonlocal problem for the system of hyperbolic equations [7,[10][11][12][13][14][15][18][19][20]28,[32][33][34][35]. Sufficient conditions for existence of unique classical solution to the investigated problem were established in the terms of initial data, and the algorithms for finding solutions are constructed under assumption on the continuity of coefficients of system (1.1).…”

“…Inverse problems for equations and systems of hyperbolic type are investigated by many authors, the bibliography and references can be found in [12,[18][19][20]24,29,32]. Methods for solving some classes of inverse problems for hyperbolic equations with mixed derivatives are proposed in [11][12][13][14][15].…”