Sanchez, ArielIagar, Razvan Gabriel2024-02-072024-02-072022-06-16Iagar, Razvan & Sanchez, Ariel. (2022). Anomalous self-similar solutions of exponential type for the subcritical fast diffusion equation with weighted reaction. Nonlinearity. 35. 3385-3416. 10.1088/1361-6544/ac72e7.0951-7715https://hdl.handle.net/10115/29838We prove existence and uniqueness of the branch of the so-called anomalous eternal solutions in exponential self-similar form for the subcritical fast-diffusion equation with a weighted reaction term ∂ t u = Δ u m + | x | σ u p , posed in R N with N ⩾ 3, where 1,$> 0 < m < m c = N − 2 N , p > 1 , and the critical value for the weight σ = 2 ( p − 1 ) 1 − m . The branch of exponential self-similar solutions behaves similarly as the well-established anomalous solutions to the pure fast diffusion equation, but without a finite time extinction or a finite time blow-up, and presenting instead a change of sign of both self-similar exponents at m = m s = ( N − 2)/( N + 2), leading to surprising qualitative differences. In this sense, the reaction term we consider realizes a perfect equilibrium in the competition between the fast diffusion and the reaction effects.engAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/anomalous solutions, fast diffusion equation, exponential self-similar solutions, weighted reaction, phase plane analysis, critical exponentsinfo:eu-repo/semantics/article10.1088/1361-6544/ac72e7info:eu-repo/semantics/openAccess