Complexification phenomenon in an example of sensitive singular perturbation
Carlos A. De Souza, É. Sanchez-Palencia · Comptes Rendus Mécanique · 2004
We consider singular perturbation problems depending on a parameter ε ⩾0 such that for ε >0 the solution u ε belongs to a Sobolev space on a domain Ω , but the limit u 0 is not a distribution on Ω . A very simple model problem, solvable by Fourier transform allows us to study the complexification process of u ε as ϵ ↘ 0 . The limit holds in the topology of a space of analytical functionals.