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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  1. Aumann, G., Reelle Funktionen, Springer-Verlag Berlin-Göttingen-Heidelberg (1954). (1954) Zbl0056.05202MR0061652
  2. Brokate, M., Krejčí, P., Schnabel, H., On uniqueness in evolution quasivariational inequalities, J. Convex Anal. 11 (2004), 111-130. (2004) Zbl1061.49006MR2159467
  3. Drábek, P., Krejčí, P., Takáč, P., Nonlinear Differential Equations. Research Notes in Mathematics, Vol. 404, Chapman & Hall/CRC London (1999). (1999) MR1695376
  4. Krasnosel'skii, M. A., Pokrovskii, A. V., Systems with Hysteresis, Nauka Moscow (1983), Russian; English edition Springer 1989. (1983) MR0987431
  5. Krejčí, P., Kurzweil, J., A nonexistence result for the Kurzweil integral, Math. Bohem. 127 (2002), 571-580. (2002) Zbl1005.26005MR1942642
  6. Krejčí, P., Laurençot, Ph., Generalized variational inequalities, J. Convex Anal. 9 (2002), 159-183. (2002) Zbl1001.49014MR1917394
  7. Krejčí, P., The Kurzweil integral with exclusion of negligible sets, Math. Bohem. 128 (2003), 277-292. (2003) Zbl1051.26006MR2012605
  8. Kurzweil, J., Generalized ordinary differential equations and continuous dependence on a parameter, Czechoslovak Math. J. 7 (82) (1957), 418-449. (1957) Zbl0090.30002MR0111875
  9. Mielke, A., Rossi, R., 10.1142/S021820250700184X, Math. Models Methods Appl. Sci. 17 (2007), 81-123. (2007) Zbl1121.34052MR2290410DOI10.1142/S021820250700184X
  10. Mielke, A., Theil, F., 10.1007/s00030-003-1052-7, NoDEA, Nonlinear Differ. Equ. Appl. 11 (2004), 151-189. (2004) Zbl1061.35182MR2210284DOI10.1007/s00030-003-1052-7
  11. Moreau, J.-J., 10.1016/0022-0396(77)90085-7, J. Differ. Equations 26 (1977), 347-374. (1977) Zbl0356.34067MR0508661DOI10.1016/0022-0396(77)90085-7
  12. Rockafellar, R. T., Convex Analysis, Princeton University Press Princeton (1970). (1970) Zbl0193.18401MR0274683
  13. Schwabik, Š., On a modified sum integral of Stieltjes type, Čas. Pěst. Mat. 98 (1973), 274-277. (1973) Zbl0266.26007MR0322114
  14. Schwabik, Š., Generalized Ordinary Differential Equations. Series in Real Analysis, Vol. 5, World Scientific Publishing Co., Inc. River Edge (1992). (1992) MR1200241
  15. Tvrdý, M., Regulated functions and the Perron-Stieltjes integral, Čas. Pěst. Mat. 114 (1989), 187-209. (1989) MR1063765
  16. Tvrdý, M., Regulated functions and the Perron-Stieltjes integral, Čas. Pěst. Mat. 114 (1989), 187-209. (1989) MR1063765

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