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The Neumann boundary problem for the perturbed sine-Gordon equationdescribing the electrodynamics of Josephson junctions has been considered. Thebehavior of a viscous term, described by a higher-order derivative with smalldiffusion coefficient, is investigated. The Green function related to thelinear third order operator is determined by means of Fourier series, andproperties of rapid convergence are established. Furthermore, some classes ofsolutions of the hyperbolic equation have been determined, proving that thereexists at least one solution whose derivatives are bounded. Results prove thatdiffusion effects are bounded and tend to zero when the small diffusioncoefficient tends to zero.

On diffusion effects of the perturbed sine-Gordon equation with Neumann boundary conditions