Maximal Solutions of Singular Diffusion Equations with General Initial Data

  • Ana Rodríguez
  • Juan Luis Vázquez
Chapter
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 7)

Abstract

In the range −1 < m ≤ 0 the Cauchy problem admits infinitely many solutions if for instance U o is nonnegative and integrable. We show existence and uniqueness of a maximal solution of the problem for initial data U o M+(R), the set of nontrivial, nonnegative and locally bounded Borel measures. These solutions are characterized in terms of a suitable decay rate as |x| → ∞ (good solutions). Since we also show that every good solution defined in a strip Q T possesses a uniquely defined trace in M+(R) at t = 0, a complete theory of maximal solutions for our equation is obtained.

Keywords

Kato 

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Copyright information

© Springer Science+Business Media New York 1992

Authors and Affiliations

  • Ana Rodríguez
    • 1
  • Juan Luis Vázquez
    • 2
  1. 1.E.T.S. ArquitecturaUniversidad Politécnica de MadridMadridSpain
  2. 2.Departamento de MatemáticasUniversidad Autónoma de MadridMadridSpain

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