We prove the strict localization for a porous medium type equation with a source term, ut = ∇(uσ∇u)+uβ , x ∈ RN , N > 1, β > σ+ 1, σ > 0, in the case of arbitrary compactly supported initial functions u0. We also otain an estimate of the size of the localization in terms of the support of the initial data supp u0 and the blow-up time T . Our results extend the well-known one dimensional result ...

Cite this: The Pan African Medical Journal. 2017;27 (Supp 3):2. DOI: 10.11604/pamj.supp.2017.27.3.11627 Received: 11/01/2017 Accepted: 05/03/2017 Published: 21/06/2017

Given a locally nite open covering fC : 2 Ig of a T 4-space X we characterize all real-valued functions f 2 C(X) which admit a representation f = P 2I ' with 2 IR and a partition of unity f' : 2 Ig fulllling the restriction supp(') C. The crucial lemma concerns a particular way of extending partitions of unity in the sense of the Tietze-Urysohn theorem. As an application, we determine the class...

We arrived on the ward in the morning and heard the senior physician say: 'We need to draw blood from this patient, but because he has no veins in his hands we will need to find another place, perhaps the neck?' One of us approached the patient and drew blood from the jugular vein; he wanted to use a venous clamp to aid him, intending to tie it around the patient's neck. Another patient post pr...

Cite this: The Pan African Medical Journal. 2017;27 (Supp 1):2. DOI: 10.11604/pamj.supp.2017.27.1.12887 Received: 27/05/2017 Accepted: 27/05/2017 Published: 28/05/2017

Cite this: The Pan African Medical Journal. 2017;27 (Supp 1):1. DOI: 10.11604/pamj.supp.2017.27.1.12886 Received: 27/05/2017 Accepted: 27/05/2017 Published: 28/05/2017

Cite this: The Pan African Medical Journal. 2017;27 (Supp 2):1. DOI: 10.11604/pamj.supp.2017.27.2.12701 Received: 08/05/2017 Accepted: 08/05/2017 Published: 09/06/2017