Advertisement
Published in:
2009 | OriginalPaper | Chapter
Diffusion-transport-reaction equations
Published in: Numerical Models for Differential Problems
Publisher: Springer Milan
Activate our intelligent search to find suitable subject content or patents.
Select sections of text to find matching patents with Artificial Intelligence. powered by
Select sections of text to find additional relevant content using AI-assisted search. powered by
In this chapter, we consider problems of the following form
11.1
$$ \left\{ \begin{gathered} - div(\mu \nabla u) + b \cdot \nabla u + \sigma u = f in\Omega , \hfill \\ u = 0 on\partial \Omega , \hfill \\ \end{gathered} \right. $$
where µ, σ, f and b are given functions (or constants). In the most general case, we will suppose that µ ∈ L
∞
(Ω) with µ(x) ≥ µ
0
> 0, σ ∈ L
2
(Ω) with σ(x) ≥ 0 a.e. in Ω,b ∈ [L
∞
(Ω)]
2
withdiv(b) ∈ L
2
(Ω), and f ∈ L
2
(Ω).