Abstract

Logarithmic diffusion is observed in several fields of sciences, such as the central limit approximation of Carleman’s model based on the Boltzman equation, a model for long Van-der-Waals interactions in thin fluid films, and the evolution of conformal metric under the Ricci flow on the plane. We focus on spreading and extinction phenomena of the solution to the logarithmic diffusion equation on a line, in the presence of a logistic reaction term. A new mathematical framework will be introduced to understand the extinction and interfacial phenomena from the point of entire solutions.

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