The Dirichlet problem for the wave equation in a spherical domain
In this paper, an ill-posed Dirichlet boundary value problem for a second-order
hyperbolic equation in a spherical domain is studied. The solution is constructed using the method
of separation of variables. The main focus is on determining the conditions that ensure the existence,
uniqueness, and stability of the solution. In the proofs, a crucial role is played by the analysis of small
denominators, based on Liouville’s theorem and K. Roth’s results on Diophantine approximations
of algebraic numbers.
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