MURPHYS-HSFS-2014 - 7th International Workshop on Multi-Rate Processes & Hysteresis, 2nd International Workshop on Hysteresis and Slow-Fast Systems, April 7-11, 2014 - Abstract
Apushkinskaya, Darya
We consider equations with the simplest hysteresis operator at the right-hand side. Such equations describe the so-called processes “with memory” in which various substances interact according to the hysteresis law. We present some results concerning the optimal regularity of solutions. Our arguments are based on quadratic growth estimates for solutions near the free boundary. The talk is based on results obtained in collaboration with Nina Uraltseva. This work was supported by the Russian Foundation of Basic Research (RFBR) through the grant number 14-01-00534 and by the St. Petersburg State University grant 6.38.670.2013.