Rate independent Kurzweil processes
- Krejčí, Pavel
- Liero, Matthias
2010 Mathematics Subject Classification
- 49J40 49J53 74C15
- Rate independent process, Kurzweil integral, variational inequality
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.
- Appl. Math., 54 (2009) pp. 117--145.