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We present a cosmological model containing a cosmological constant $\Lambda$and a component with an inhomogeneous equation of state. We study the form ofthe inhomogeneous equation of state for which the model exhibits the relaxationof the cosmological constant, i.e. it asymptotically tends to the de Sitterregime characterized by a small positive effective cosmological constant. Theeffect of the relaxation of the cosmological constant is observed both fornegative and positive values of $\Lambda$ and for a range of model parameters.A special emphasis is put on the study of the details of the CC relaxationmechanism and the robustness of the mechanism to the variation of modelparameters. It is found that within the studied model the effectivecosmological constant at large scale factor values is small because theabsolute value of the real cosmological constant is large.

The inhomogeneous equation of state and the road towards the solution of the cosmological constant problem