Abstract:We consider a class of Nemytskii superposition operators that covers the nonlinear part of traveling wave models from laser dynamics, population dynamics, and chemical kinetics. Our main result is the $C^1$-continuity property of these operators over Sobolev-type spaces of periodic functions.
Keywords: Nemytskii operators, Sobolev-type spaces of periodic functions, $C^1$-smoothness
AMS Subject Classification: 47H99 46E30