An existence theorem for an implicit nonlinear evolution equation
- Bermúdez de Castro López-Varela, Alfredo
- Durany Castrillo, José
- Saguez, Christian
ISSN: 0010-0757
Year of publication: 1984
Volume: 35
Fascicle: 1
Pages: 19-34
Type: Article
More publications in: Collectanea mathematica
Abstract
In this paper we prove the existence of a solution for a non linear evolution equations of the form: $$\frac{d}{dt}B(u(t))+A(t,u(t)) \ni f(t)$$ Where $A$ and $B$ are nonlinear operators, possibly multivalued.\newline\newline The proof is based on implicit discretization in time and passing to the limit as the time step goes to zero.\newline An application to a Stefan problem, arising from the solidification of a metal in a mould, is given.