Ecuaciones en derivadas parciales gobernadas por operadores acretivos

Resumen

Una teoría que ha resultado ser de gran utilidad en el estudio de muchas ecuaciones en derivadas parciales no lineales es la teoría de semigrupos no lineales generados por operadores acretivos en espacios de Banach. Dicha teoría se basa fundamentalmente en el Teorema de Crandall-Ligget y en las aportaciones de Ph. Bénilan. En este artículo, después de hacer una exposición esquemática de esta teoría general, veremos cómo la hemos aplicado a algunas ecuaciones en derivadas parciales no lineales que aparecen en diversos campos de la Ciencia.

Abstract

A theory which has become very useful in the study of a great deal of non-linear partial differential equations is the theory of non-linear semigroups generated by accretive operators in Banach spaces. This theory is fundamentally based on Cradall-Liggett’s Theorem and also on the work of Ph. Bénilan. In this paper, after a schematic exposition of this general theory, we shall see how we have applied it to some non-linear partial differential equations that appear in several scientific fields.

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Correspondence to José M. Mazón Ruiz.

Additional information

A la memoria de Fuensanta Andreu, con quien compartí los resultados de este trabajo y de Philippe Bénilan, que nos introdujo en las ecuaciones de evolución.

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Mazón Ruiz, J.M. Ecuaciones en derivadas parciales gobernadas por operadores acretivos. SeMA 52, 11–39 (2010). https://doi.org/10.1007/BF03322573

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Palabras clave

  • Operadores acretivos
  • ecuaciones de evolución
  • semigrupos de operadores
  • ecuaciones parabólicas cuasi-lineales

Clasificación por materias AMS

  • 47H20
  • 47J35
  • 47B44
  • 35K59