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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

Initial Data Cauchy Problem Borel Measure Harnack Inequality Maximal Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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