13 citations · 16 across the 5 of their papers we have counts for
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Properties of the phase boundary in the parabolic problem with hysteresis
Darya Apushkinskaya, Sergey Tikhomirov, Nina Uraltseva
We study solutions of parabolic equations with a discontinuous hysteresis operator, described by a free interface boundary. It is established that for spatially transverse initial…
Free boundaries in problems with hysteresis
D. E. Apushkinskaya, N. N. Uraltseva
In this note we present a survey concerning parabolic free boundary problems involving a discontinuous hysteresis operator. Such problems describe biological and chemical processes…
Equilibrium points of a singular cooperative system with free boundary
John Andersson, Henrik Shahgholian, Nina N. Uraltseva +1
In this paper we initiate the study of maps minimising the energy which, due to Lipschitz character of the integrand, gives rise to the si…
Uniform estimates near the initial state for solutions to the two-phase parabolic problem
D. E. Apushkinskaya, N. N. Uraltseva
This paper is devoted to a proof of optimal regularity, near the initial state, for weak solutions to the two-phase parabolic obstacle problem. The approach used here is general en…
The Parabolic Two-Phase Membrane Problem: Regularity in Higher Dimensions
Henrik Shahgholian, Nina Uraltseva, Georg S. Weiss
For the parabolic obstacle-problem-like equation where and are positive Lipschitz functions, we prove in arb…