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We study systems of reaction-diffusion equations with discontinuous spatially distributed hysteresis on the right-hand side. The input of the hysteresis is given by a vector-valued function of space and time. Such systems describe hysteretic interaction of non-diffusive (bacteria, cells, etc.) and diffusive (nutrient, proteins, etc.) substances leading to formation of spatial patterns. We provide sufficient conditions under which the problem is well posed in spite of the assumed discontinuity of...
An existence and regularity theorem is proved for integral equations of convolution type which contain hysteresis nonlinearities. On the basis of this result, frequency-domain stability criteria are derived for feedback systems with a linear infinite-dimensional system in the forward path and a hysteresis nonlinearity in the feedback path. These stability criteria are reminiscent of the classical circle criterion which applies to static sector-bounded nonlinearities. The class of hysteresis operators...
An existence and regularity theorem is proved for integral equations
of convolution type which contain hysteresis nonlinearities. On
the basis of this result, frequency-domain stability criteria are
derived for feedback systems with a linear infinite-dimensional
system in the forward path and a hysteresis nonlinearity in the
feedback path. These stability criteria are reminiscent of the
classical circle criterion which applies to static sector-bounded
nonlinearities. The class of hysteresis operators...
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