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Evolution equations generated by subdifferentials in the dual space of $(H^1(\Omega))$

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  • This paper is concerned with the subdifferential operator approach to nonlinear (possibly degenerate and singular) parabolic PDE's of the form $u_t-\Delta \beta(u) \ni f$ formulated in the dual space of $H^1(\Omega)$, where $\beta$ is a maximal monotone graph in $\mathbf R\times \mathbf R$. In the set-up considered so far [8], some coerciveness condition has been required for $\beta$, corresponding at least to the fact that it is onto $\mathbf R$. In the present paper, we show that the subdifferential operator approach is possible for any maximal monotone graph $\beta$ without any growth condition.
    Mathematics Subject Classification: 80A22, 35A15, 35K05, 35K85, 35R35.


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