In this paper we deal with the mathematical investigation of a class of parabolic partial differential equations containing a continuous hysteresis operator arising in the context of magnetohydrodynamics. The main result we achieve is the existence of a weak solution by means of a technique based on an implicit time discretization scheme. Uniqueness is obtained under some suitable monotonicity assumptions on the hysteresis operator; finally we also analyse the dependence of the solution on the data.
Wellposedness results for a class of parabolic partial differential equations with hysteresis / Eleuteri, Michela. - In: NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS. - ISSN 1021-9722. - 15:(2008), pp. 557-580. [10.1007/s00030-008-7018-z]
Wellposedness results for a class of parabolic partial differential equations with hysteresis
ELEUTERI, Michela
2008
Abstract
In this paper we deal with the mathematical investigation of a class of parabolic partial differential equations containing a continuous hysteresis operator arising in the context of magnetohydrodynamics. The main result we achieve is the existence of a weak solution by means of a technique based on an implicit time discretization scheme. Uniqueness is obtained under some suitable monotonicity assumptions on the hysteresis operator; finally we also analyse the dependence of the solution on the data.
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