On Degenerate Nonlinear Parabolic Equations on the Bohr Compactum

Abstract: A formulation of spatially almost periodic (in the sense of Besicovitch) solutions ofdegenerate nonlinear parabolic equations is given in the framework of the theory of differentialequations on the Bohr compact group. The concept of a generalized entropy solution of theCauchy problem is introduced, and its existence and uniqueness are proved. To prove uniqueness,a version of Kruzhkov’s doubling variable method is developed. This formulation is useful fordescribing new invariant transformations on the set of entropy solutions (generalized shifts). © 2022, Pleiades Publishing, Ltd.