Elliptic-Parabolic Equation with Absorption of Obstacle type

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Abstract This paper is concerned with existence and uniqueness of solutions for a doubly nonlinear degenerate parabolic problem of the type β(w) t − div a(x, Dw) + ∂ j ( ., β(w) ) ∋ f, where α is a Leray-Lions operator, β is a nondecreasing continuous function and ∂ j(., r) is a maximal monotone graph with respect to r defined on a closed interval of ℝ. Particular cases of j correspond to the so called obstacle problem.

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