An existence result for a p.d.e. with hysteresis, convection and a nonlinear boundary condition. (English) Zbl 1163.35458

Summary: A partial differential equation containing a continuous hysteresis operator and a convective term is considered. This model equation, which appears in the context of magnetohydrodynamics, is coupled with a nonlinear boundary condition containing a memory operator. Under suitable assumptions, an existence result is achieved using an implicit time discretization scheme.


35Q35 PDEs in connection with fluid mechanics
47J40 Equations with nonlinear hysteresis operators
76E06 Convection in hydrodynamic stability
34B15 Nonlinear boundary value problems for ordinary differential equations
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