Abstract
AbstractWe present an existence result for an evolution equation with a nonlinear operator, which is a composition of two monotone mappings. The first monotone mapping is a subdifferential of the indicator function of some convex set while the other is constructed as the Nemyckii operator of a monotone function. Such equations arise from the mathematical models, which describe piezoelectric material behavior. Under some additional assumptions we prove the existence and uniqueness of the strong solution for the case, when the operator generated by the monotone function is a Lipschitz continuous mapping. In the case of a nonlinear growth of the monotone function we prove the existence of the strong solution (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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