Displaying similar documents to “ BV solutions of rate independent differential inclusions”

Rate independent Kurzweil processes

Pavel Krejčí, Matthias Liero (2009)

Applications of Mathematics

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The Kurzweil integral technique is applied to a class of rate independent processes with convex energy and discontinuous inputs. We prove existence, uniqueness, and continuous data dependence of solutions in B V spaces. It is shown that in the context of elastoplasticity, the Kurzweil solutions coincide with natural limits of viscous regularizations when the viscosity coefficient tends to zero. The discontinuities produce an additional positive dissipation term, which is not homogeneous...

A remark on the local Lipschitz continuity of vector hysteresis operators

Pavel Krejčí (2001)

Applications of Mathematics

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It is known that the vector stop operator with a convex closed characteristic Z of class C 1 is locally Lipschitz continuous in the space of absolutely continuous functions if the unit outward normal mapping n is Lipschitz continuous on the boundary ∂ Z of Z . We prove that in the regular case, this condition is also necessary.

Continuity of hysteresis operators in Sobolev spaces

Pavel Krejčí, Vladimír Lovicar (1990)

Aplikace matematiky

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We prove that the classical Prandtl, Ishlinskii and Preisach hysteresis operators are continuous in Sobolev spaces W 1 , p ( 0 , T ) for 1 ≤ p < + ∞ , (localy) Lipschitz continuous in W 1 , 1 ( 0 , T ) and discontinuous in W 1 , ∞ ( 0 , T ) for arbitrary T > 0 . Examples show that this result is optimal.