Abstract
We investigate nonlinear parabolic variational inequalities which contain functional dependence on the unknown function. Such parabolic functional differential equations were studied e.g. by L. Simon in [8] (which was motivated by the work of M. Chipot and L. Molinet in [4]), where the following equation was considered:
where V denotes a closed linear subspace of the Sobolev-space W 1,p(Ω) (2 ≦ p < ∞). In the above mentioned paper existence of weak solutions of the above equation is shown. These results were extended to systems of functional differential equations in [2]. In the following, we extend these existence results to variational inequalities by using the (less known) results of [6]. Finally, we show some examples.
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This work was supported by the Hungarian National Foundation for Scientific Research under grant OTKA T 049819.
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Besenyei, Á. On nonlinear parabolic variational inequalities containing nonlocal terms. Acta Math Hung 116, 145–162 (2007). https://doi.org/10.1007/s10474-007-6024-7
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DOI: https://doi.org/10.1007/s10474-007-6024-7