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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
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