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Abstract: We consider a simplified model of methane hydrates which we cast as a nonlinear evolution problem. For its well-posedness we extend the existing theory to cover the case in which the problem involves a measurable family of graphs. We represent the nonlinearity as a subgradient and prove a useful comparison principle, thus optimal regularity results follow. For the numerical solution we apply a fully implicit scheme without regularization and use the semismooth Newton algorithm for a solver, and the graph is realized as a complementarity constraint (CC). The algorithm is very robust and we extend it to define an easy and superlinearly convergent fully implicit scheme for the Stefan problem and other multivalued examples. [Copyright &y& Elsevier]