Weak long-range diffusion

We study the spreading solutions of the nonlinear diffusion equation 𝑐𝑡 = [(𝜈 + 𝑐)𝑐𝑥]𝑥 when the far-field diffusivity 𝜈 is small. The method of strained coordinates is used to construct a uniform asymptotic correction to the similarity solution of the unperturbed problem. The equation provides a possible analogue to similar models of fluid jets and plumes.