Geodesic
Properties of the phase boundary in the parabolic problem with hysteresis
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 51, Tome 536 (2024), pp. 26-53

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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 data from the space $W^{2-2/q}_q$ with $q > 3$, there exists a solution in the space $W^{2,1}_q$, where the interface boundary exhibits Holder continuity with an exponent of $1/2$. Furthermore for initial data from the space $W^2_\infty$, it is proven that the interface boundary satisfies the Lipschitz condition. It is shown that for non-transversal initial data, solutions with an interface boundary do not exist. 
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     author = {D. E. Apushkinskaya and S. B. Tikhomirov and N. N. Uraltseva},
     title = {Properties of the phase boundary in the parabolic problem with hysteresis},
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     pages = {26--53},
     publisher = {mathdoc},
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     year = {2024},
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D. E. Apushkinskaya; S. B. Tikhomirov; N. N. Uraltseva. Properties of the phase boundary in the parabolic problem with hysteresis. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 51, Tome 536 (2024), pp. 26-53. http://geodesic.mathdoc.fr/item/ZNSL_2024_536_a2/