The porous medium equation with blowing up boundary data
The porous medium equation with blowing up boundary data
Authors
Venegas Torres, Osvaldo
Authors
Date
2012-02-23
Datos de publicación:
Advanced Nonlinear Studies, Vol.9, N°1, 1-27, 2009
Keywords
Teoría matemática - Modelos numéricos
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Abstract
We study the blow-up set of a solution u(x,t) to the porous medium equation, ut = δ(um), in ω x (0,T) for two different boundary conditions, u(x,t)=f (x)/(T - t)1/m-xor -∂um/∂n̂(x,t) = g(x)/(T - t)m/m-1 on ∂ω× (0,T). Here m > 1 and ω is a bounded smooth domain in ℝN. We establish point-wise and integral conditions on f and g respectively in order to obtain regional or global blow-up.