Global in time existence and uniqueness of classical solutions to a certain nonlinear parabolic partial differential equation, containing an integral term, are proved. Smoothness regularity and time-independent estimates for all partial derivatives are also obtained. Such an equation is of a non-standard type, and governs the time evolution of certain populations of infinitely many nonlinearly coupled random oscillators, described by a model first proposed by Kuramoto and Sakaguchi.
"Existence and uniqueness of solutions to the Kuramoto-Sakaguchi nonlinear parabolic integrodifferential equation." Differential Integral Equations 13 (4-6) 649 - 667, 2000. https://doi.org/10.57262/die/1356061243