We deal in detail with the question of existence, uniqueness and asymptotic behaviour of solutions to a parabolic equation with hysteresis and convection. This equation is part of a model system which describes the magnetohydrodynamic (MHD) flow of a conducting fluid between two ferromagnetic plates.The result of this paper complements the content of a previous paper of the first author, where existence of the solution has been proved under fairly general assumptions on the hysteresis operator and the uniqueness was only obtained for a restricted class of hysteresis operators.
Uniqueness and decay estimates for a class of parabolic partial differential equations with hysteresis and convection / Eleuteri, Michela; Kopfová, Jana. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - 73:1(2010), pp. 48-65. [10.1016/j.na.2010.02.028]
Uniqueness and decay estimates for a class of parabolic partial differential equations with hysteresis and convection
ELEUTERI, Michela;
2010
Abstract
We deal in detail with the question of existence, uniqueness and asymptotic behaviour of solutions to a parabolic equation with hysteresis and convection. This equation is part of a model system which describes the magnetohydrodynamic (MHD) flow of a conducting fluid between two ferromagnetic plates.The result of this paper complements the content of a previous paper of the first author, where existence of the solution has been proved under fairly general assumptions on the hysteresis operator and the uniqueness was only obtained for a restricted class of hysteresis operators.
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