Existence of a solution to the nonhomogeneous ultrahyperbolic equation

M. N. Demchenko

Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 54, Tome 533 (2024), pp. 77-100

Résumé

The nonhomogeneous ultrahyperbolic equation in ${\mathbb R}^d\times{\mathbb R}^n$ is considered. An additional condition prescribing the behavior of a solution to the equation at the infinity is proposed. It is proved that the problem for the equation in consideration with such a condition is not overdetermined. The solution is given in a form of a singular integral, and the corresponding asymptotics is found with the use of the stationary phase method.

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