Bermudez, A.; Durany, J.; Saguez, C. An existence theorem for an implicit nonlinear evolution equation. (English) Zbl 0584.47060 Collect. Math. 35, 19-34 (1984). 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. Cited in 9 Documents MSC: 47H20 Semigroups of nonlinear operators 47F05 General theory of partial differential operators 35F25 Initial value problems for nonlinear first-order PDEs Keywords:multivalued operator; nonlinear evolution equation; implicit discretization in time; Stefan problem PDFBibTeX XMLCite \textit{A. Bermudez} et al., Collect. Math. 35, 19--34 (1984; Zbl 0584.47060) Full Text: EuDML