Degenerate Nonlinear Diffusion Equations by Angelo Favini & Gabriela Marinoschi

Author:Angelo Favini & Gabriela Marinoschi
Language: eng
Format: epub
Publisher: Springer Berlin Heidelberg, Berlin, Heidelberg

(2.112)

with C a constant. Thus, we have to deal with the equation

(2.113)

where A 0 is the restriction of A Δ on L 2(Ω), A 0 : D(A 0) ⊂ L 2(Ω) → L 2(Ω),

First, we shall consider that g ∈ L 2(Ω). The linear operator A 0 : V → V ′ is continuous and coercive, so its realization on L 2(Ω) is m-accretive (see [14], pp. 36). Also, the realization of G on L 2(Ω) is maximal monotone on L 2(Ω). Hence, we define G + A 0 : D(A + G 0) ⊂ L 2(Ω) → L 2(Ω), where

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