## Existence of solutions for degenerate sweeping processes.(English)Zbl 0884.34019

Authors’ abstract: The existence of solutions to a class of non-standard sweeping processes of the form $-u'(t)\in \partial\delta_{C(t)}(Au(t))$ is established. In contrast to the “classical” sweeping process with $$A=\text{id}$$, these problems may be degenerate, since there might be no solutions at all.

### MSC:

 34A60 Ordinary differential inclusions 35G10 Initial value problems for linear higher-order PDEs 35K25 Higher-order parabolic equations 74B20 Nonlinear elasticity

### Keywords:

elastoplasticity; sweeping process
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