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An existence theorem for an implicit nonlinear evolution equation. (English) Zbl 0584.47060

We prove the existence of a solution for a nonlinear evolution equation of the form: \((d/dt)B(u(t))+A(t,u(t))\ni f(t)\), where A and B are nonlinear operators, possibly multivalued. The proof is based on implicit discretization in time and passing to the limit as the time step goes to zero. An application to a Stefan problem, arising from the solidification of a metal in a mould, is given.

MSC:

47H20 Semigroups of nonlinear operators
47F05 General theory of partial differential operators
35F25 Initial value problems for nonlinear first-order PDEs
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