Geodesic
Rate independent Kurzweil processes
Applications of Mathematics, Tome 54 (2009) no. 2, pp. 117-145

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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 $BV$ 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.
DOI : 10.1007/s10492-009-0009-5
Classification : 49J40, 49K40, 74C15
Keywords: Kurzweil integral; rate independence 
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Krejčí, Pavel; Liero, Matthias. Rate independent Kurzweil processes. Applications of Mathematics, Tome 54 (2009) no. 2, pp. 117-145. doi: 10.1007/s10492-009-0009-5

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