chapter  22
6 Pages

The Kuramoto-Sakaguchi Nonlinear Parabolic Integrodifferential Equation 1

ByMikhail Lavrentiev, R. Spigler

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.