An existence theorem for an implicit nonlinear evolution equation

  1. Bermúdez de Castro López-Varela, Alfredo
  2. Durany Castrillo, José
  3. Saguez, Christian
Revista:
Collectanea mathematica

ISSN: 0010-0757

Ano de publicación: 1984

Volume: 35

Fascículo: 1

Páxinas: 19-34

Tipo: Artigo

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Outras publicacións en: Collectanea mathematica

Resumo

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.

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