FORMULATION OF THE INITIAL-BOUNDARY VALUE PROBLEM IN A CIRCULAR DOMAIN

Abstract

This paper is devoted to the formulation of an initial-boundary value problem in a circular domain for partial differential equations arising in mathematical physics. The circular geometry is described using polar coordinates, which allows an explicit representation of the governing equations and boundary conditions. Particular attention is paid to the consistent specification of initial and boundary conditions required to ensure the well-posedness of the problem in the sense of Hadamard. The role of domain symmetry in simplifying the analytical treatment is emphasized, and the applicability of classical methods such as separation of variables and spectral analysis of the Laplace operator is discussed. The proposed formulation provides a rigorous mathematical foundation for further analytical and numerical studies of wave propagation and related physical processes in circular domains.