Free boundaries in problems with hysteresis
Darya Evgen'evna Apushkinskaya, Nina Nikolaevna Ural'tseva · Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences · 2015
Here, we present a survey concerning parabolic free boundary problems involving a discontinuous hysteresis operator. Such problems describe biological and chemical processes 'with memory' in which various substances interact according to hysteresis law. Our main objective is to discuss the structure of the free boundaries and the properties of the so-called 'strong solutions' belonging to the anisotropic Sobolev class [Formula: see text] with sufficiently large q. Several open problems in this direction are proposed as well.