ABSTRACT
This chapter discusses parabolic equations for a two-dimensional bounded medium. It considers rectangular and circular domains. Eigenvalues and eigenfunctions of the boundary value problem depend on the types of boundary conditions. A heat-conducting, thin, uniform, circular plate of radius l is thermally insulated over its lateral faces. The boundary of the plate is kept at constant zero temperature, and the initial temperature distribution within the plate is zero. An analogous phenomenon exists when alternating current flows in a metal conductor. Alternating current does not flow through a conductor with a uniform cross-sectional profile but concentrates close to the conductor surface.
