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Hysteresis filtering in the space of bounded measurable functions. (English) Zbl 1177.35125
Summary: We define a mapping which with each function \(u \in L^{\infty} (0,T)\) and an admissible value of \(r>0\) associated the function \(\xi\) with a prescribed initial condition \(\xi^0\) which minimizes the total variation in the \(r\)-neighborhood of \(u\) in each subinterval \([0,t]\) of \([0,T]\). We show that this mapping is non-expansive with respect to \(u,r\) and \(\xi^0\), and coincides with the so-called play operator if \(u\) is a regulated function.

MSC:
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
74N30 Problems involving hysteresis in solids
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