Classical solutions to the one‐dimensional logarithmic diffusion equation with nonlinear Robin boundary conditions

Abstract

In this paper, we investigate the behavior of classical solutions to the onedimensional (1D) logarithmic diffusion equation with nonlinear Robin boundary conditions, namely,where γ is a constant. Let u 0 > 0 be a smooth function defined on [ − l, l], and which satisfies the compatibility condition 𝜕 𝑥 log 𝑢 0 (±𝑙) = ±2𝛾𝑢𝑝−1 0 (±𝑙).