Erschienen in:

1997 | OriginalPaper | Buchkapitel

Nonlinear Parabolic Operators

verfasst von : Alexander Pankov

Erschienen in: G-Convergence and Homogenization of Nonlinear Partial Differential Operators

Verlag: Springer Netherlands

Enthalten in: Professional Book Archive

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Let Q₀ ⊂ Rn be a bounded open set and Q = (0, T) × Q₀. On Q, we shall consider evolution operators of the form 4.1.1$$\angle u = {\partial _t}u - div a(t,x,u,\nabla u) + {a_0}(t,x,u,\nabla u),$$ where ∂_t = ∂/∂t. We assume that the functions $$a:Q \times R \times {R^n} \to {R^n}$$ and $${a_0}:Q \times R \times {R^n} \to R$$ satisfy the Catathéodory condition and the following inequalities:

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