Assume that Ω is a bounded domain in Rn with n ≥ 2. We study positive solutions to the problem, ∆u = up in Ω, u(x)→∞ as x→ ∂Ω, where p > 1. Such solutions are called boundary blow-up solutions of ∆u = up. We show that a boundary blow-up solution exists in any bounded domain if 1 < p < n n−2 . In particular, when n = 2, there exists a boundary blow-up solution to ∆u = up for all p ∈ (1,∞). We al...

The Network of Noisy Leaky Integrate and Fire (NNLIF) model describes the behavior of a neural network at mesoscopic level. It is one of the simplest self-contained mean-field models considered for that purpose. Even so, to study the mathematical properties of the model some simplifications were necessary [4, 5, 6], which disregard crucial phenomena. In this work we deal with the general NNLIF ...

Formation of hydrates is observed during drilling and construction of wells, more frequently in gas wells located offshore (deep sea water). Hydrates of natural gas can clog chokes and kill lines, and obstruct the opening or closure of blow out preventer (BOP), seal well override valve and immobilize well string. Because of that, this work was mainly focused in the selection and adaptation of a...