Rate independent Kurzweil processes

Pavel Krejčí; Matthias Liero

Applications of Mathematics (2009)

  • Volume: 54, Issue: 2, page 117-145
  • ISSN: 0862-7940

Abstract

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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 of degree one.

How to cite

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Krejčí, Pavel, and Liero, Matthias. "Rate independent Kurzweil processes." Applications of Mathematics 54.2 (2009): 117-145. <http://eudml.org/doc/37812>.

@article{Krejčí2009,
abstract = {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 $BV$ 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 of degree one.},
author = {Krejčí, Pavel, Liero, Matthias},
journal = {Applications of Mathematics},
keywords = {Kurzweil integral; rate independence; Kurzweil integral; rate independence},
language = {eng},
number = {2},
pages = {117-145},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Rate independent Kurzweil processes},
url = {http://eudml.org/doc/37812},
volume = {54},
year = {2009},
}

TY - JOUR
AU - Krejčí, Pavel
AU - Liero, Matthias
TI - Rate independent Kurzweil processes
JO - Applications of Mathematics
PY - 2009
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 54
IS - 2
SP - 117
EP - 145
AB - 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 $BV$ 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 of degree one.
LA - eng
KW - Kurzweil integral; rate independence; Kurzweil integral; rate independence
UR - http://eudml.org/doc/37812
ER -

References

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  12. Rockafellar, R. T., Convex Analysis, Princeton University Press Princeton (1970). (1970) Zbl0193.18401MR0274683
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  16. Tvrdý, M., Regulated functions and the Perron-Stieltjes integral, Čas. Pěst. Mat. 114 (1989), 187-209. (1989) MR1063765

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