Abstract
The Crandall-Liggett theorem is applied to $${{\partial u} \mathord{\left/ {\vphantom {{\partial u} {\partial t}}} \right. \kern-\nulldelimiterspace} {\partial t}} = \sum\limits_{i = 1}^n {\partial (\varphi _i (x,\nabla u))/\partial x_i } + f(x,u)$$ with various boundary conditions. Moreover, the ellipticity of the operator on the right hand side is allowed to degenerate (mildly) on the spatial boundary.
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