An existence theorem for an implicit nonlinear evolution equation

• Autores: Alfredo Bermúdez de Castro y López-Varela, José Durany Castrillo, Christian Saguez
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 35, Fasc. 1, 1984, págs. 19-34
• Idioma: inglés
• Títulos paralelos:
  • Un teorema de existencia para una ecuación de evolución implicita no lineal
• Enlaces
  • Texto completo
• Resumen

  • 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.