Existence, uniqueness, and regularity for the Kuramoto-Sakaguchi equation with unboundedly supported frequency distribution. (Q2343871)

The Fokker-Planck-type Kuramoto-Sakaguchi nonlinear parabolic integro-differential equation is considered when the ``frequency distribution'', the frequency being an independent variable in the model equation, has unbounded support. Existence, uniqueness, and regularity of solutions are established here, taking suitable limits in the formulation of the previously studied problem, where the aforementioned support was assumed to be bounded. The paper is organized as follows. Section 1 is an introduction. In Section 2, the governing equation and the main assumptions are given. The model equation on unbounded domain with compactly supported frequency distribution is studied in Section 3. Section 4 is devoted to the investigation of the model equation with unboundedly supported frequency distribution. Uniqueness of solutions to the problem stated in Section 2 is established in Section 5.