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Keywords:
Kurzweil integral; rate independence
Kurzweil integral; rate independence
Summary:
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.
References:
[1] Aumann, G.: Reelle Funktionen. Springer-Verlag Berlin-Göttingen-Heidelberg (1954). MR 0061652 | Zbl 0056.05202
[2] Brokate, M., Krejčí, P., Schnabel, H.: On uniqueness in evolution quasivariational inequalities. J. Convex Anal. 11 (2004), 111-130. MR 2159467 | Zbl 1061.49006
[3] Drábek, P., Krejčí, P., Takáč, P.: Nonlinear Differential Equations. Research Notes in Mathematics, Vol. 404. Chapman & Hall/CRC London (1999). MR 1695376
[4] Krasnosel'skii, M. A., Pokrovskii, A. V.: Systems with Hysteresis. Nauka Moscow (1983), Russian; English edition Springer 1989. MR 0987431
[5] Krejčí, P., Kurzweil, J.: A nonexistence result for the Kurzweil integral. Math. Bohem. 127 (2002), 571-580. MR 1942642 | Zbl 1005.26005
[6] Krejčí, P., Laurençot, Ph.: Generalized variational inequalities. J. Convex Anal. 9 (2002), 159-183. MR 1917394 | Zbl 1001.49014
[7] Krejčí, P.: The Kurzweil integral with exclusion of negligible sets. Math. Bohem. 128 (2003), 277-292. MR 2012605 | Zbl 1051.26006
[8] Kurzweil, J.: Generalized ordinary differential equations and continuous dependence on a parameter. Czechoslovak Math. J. 7 (82) (1957), 418-449. MR 0111875 | Zbl 0090.30002
[9] Mielke, A., Rossi, R.: Existence and uniqueness results for a class of rate-independent hysteresis problems. Math. Models Methods Appl. Sci. 17 (2007), 81-123. DOI 10.1142/S021820250700184X | MR 2290410 | Zbl 1121.34052
[10] Mielke, A., Theil, F.: On rate-independent hysteresis models. NoDEA, Nonlinear Differ. Equ. Appl. 11 (2004), 151-189. DOI 10.1007/s00030-003-1052-7 | MR 2210284 | Zbl 1061.35182
[11] Moreau, J.-J.: Evolution problem associated with a moving convex set in Hilbert space. J. Differ. Equations 26 (1977), 347-374. DOI 10.1016/0022-0396(77)90085-7 | MR 0508661 | Zbl 0356.34067
[12] Rockafellar, R. T.: Convex Analysis. Princeton University Press Princeton (1970). MR 0274683 | Zbl 0193.18401
[13] Schwabik, Š.: On a modified sum integral of Stieltjes type. Čas. Pěst. Mat. 98 (1973), 274-277. MR 0322114 | Zbl 0266.26007
[14] Schwabik, Š.: Generalized Ordinary Differential Equations. Series in Real Analysis, Vol. 5. World Scientific Publishing Co., Inc. River Edge (1992). MR 1200241
[15] Tvrdý, M.: Regulated functions and the Perron-Stieltjes integral. Čas. Pěst. Mat. 114 (1989), 187-209. MR 1063765
[16] Tvrdý, M.: Regulated functions and the Perron-Stieltjes integral. Čas. Pěst. Mat. 114 (1989), 187-209. MR 1063765
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