Solutions with snaking singularities for the fast diffusion equation
Марек Фила, John R. King, Jin Takahashi, Eiji Yanagida · Transactions of the American Mathematical Society · 2021
We construct solutions of the fast diffusion equation, which exist for all t ∈ R t\in \mathbb {R} and are singular on the set Γ ( t ) ≔ { ξ ( s ) ; − ∞ > s ≤ c t } \Gamma (t)≔\{ \xi (s) ; -\infty >s \leq ct \} , c > 0 c>0 , where ξ ∈ C 3 ( R ; R n ) \xi \in C^3(\mathbb {R};\mathbb {R}^n) , n ≥ 2 n\geq 2 . We also give a precise description of the behavior of the solutions near Γ ( t ) \Gamma (t) .